Regression Discontinuinty Designs

The key concept

A threshold in a continuous variable determines treatment assignment

Running variable (or “score”), X: a continuously distributed variable with a clearly defined cutoff (c) that determines which units are assigned to treatment and which ones are assigned to control.

Prior to the treatment, the outcome should not differ between the treatment and control group (continuity assumption). The distribution of the variable which indicates the threshold should have no jumps around this cutoff value.

Example using an arbitrary test score cut-off for being enrolled in tutoring programs on learning outcomes, from Andrew Heiss

Theory

There are two different variants of the RDD:

• sharp RDD: the threshold separates the treatment and control group exactly

• fuzzy RDD: the threshold influences the probability of being treated. this is in fact an instrumental variable approach (estimating a Local Average Treatment Effect [LATE])

The value of the outcome (Y) for individuals just below the threshold is the missing counterfactual outcome. It increases continuously with the cutoff variable, as opposed to the treatment.

Here are some nice elaborations and fifures on these two variants of RDD from the World Bank

Sharp vs Fuzzy RDD illustration from the World Bank

Sharp RDD

"In sharp designs, the probability of treatment changes from 0 to 1 at the cutoff. There are no cross-overs and no non-complance. For example, if a scholarship award is given to all students above a threshold test score of 80%, then the assignment rule defines treatment status deterministically with probabilities of 0 or 1. Thus, the design is sharp.

Fuzzy RDD

In fuzzy designs, the probability of treatment is discontinuous at the cutoff, but not to the degree of a definitive 0 to 1 jump. For example, if food stamp eligibility is given to all households below a certain income, but not all households receive the food stamps, then the assignment rule defines treatment status probabilistically but not perfectly. Thus, the design is fuzzy. The fuzziness may result from imperfect compliance with the law/rule/program; imperfect implementation that treated some non-eligible units or neglected to treat some eligible units; spillover effects; or manipulation of the eligibility index.

A fuzzy design assumes that, in the absence of the assignment rule, some of those who take up the treatment would not have participated in the program. The eligibility index acts as a nudge. The subgroup that participates in a program due to the selection rule is called compliers (see e.g. Angrist and Imbens (1994), and Imbens, Angrist, and Rubin (1996)); under the RDD, the treatment effects are estimated only for the group of compliers."

Advantages of RDD

With an RDD approach some assumptions can be tested. Individuals or units close to the threshold are nearly identical, except for characteristics which are affected by the treatment.

RDD’s strengths include that we can:

• illustrate the design graphically
• test some of the underlying assumptions and support arguments through data visualization
• reliably (unbiased) estimates local average treatment effects
• include relevant confounders in model

Application Demo

Load required packages. In this demo, we will use the package “rdrobust”

install.packages("rdrobust",
                 repos = "http://cran.us.r-project.org")

## 
## The downloaded binary packages are in
##  /var/folders/_c/txgkq4nd3pqfrsyx1ygqk9kh0000gq/T//RtmpYfx373/downloaded_packages

install.packages("rddensity",
                 repos = "http://cran.us.r-project.org")

## 
## The downloaded binary packages are in
##  /var/folders/_c/txgkq4nd3pqfrsyx1ygqk9kh0000gq/T//RtmpYfx373/downloaded_packages

library(tidyverse)  # ggplot(), %>%, mutate(), and friends
# library(broom)  # Convert models to data frames
library(rdrobust)  # For robust nonparametric regression discontinuity
library(rddensity)  # For nonparametric regression discontinuity density tests
library(modelsummary)  # Create side-by-side regression tables

Simulate data for demo

Demo Question: fishing mortality on crabs

We are interested in the causal effect of fishing on crab mortality. This question is surprisingly hard to answer because it’s hard to tease apart natural mortality from fishing mortality, but it is an important effect to estimate for fisheries management.

### Make column for observation ID
crab_data <- data.frame(id = seq(1, 1000),
                 
                 ### Add columns for explanatory variables
                 
                 ### Add column for treatment variable
                 fished = c(rep(0, 500), rep(1, 500)),
                 
                 ### Add column for body size
                 size = c(runif(500, min = 10, max = 80),
                          runif(500, min = 60, max = 130)),
                 
                 ### And the rest of the covariates
                 sst = runif(1000, min = 10, max = 16),
                 salinity = runif(1000, min = 1, max = 10),
                 npp = runif(1000, min = 0, max = 1),
                 
                 ### And the error term
                 error = rnorm(1000, mean = 0, sd = 2))

### Visualize
ggplot(crab_data) +
  geom_boxplot(aes(x = size, group = fished)) +
  geom_vline(xintercept = 70)

### center size at legal catch size
crab_data <- crab_data %>%
  mutate(size_centered = size - 70)
  
### Make column for outcome variable (total mortality) 
crab_data <- crab_data %>%
  mutate(natural_mortality = 10 + -0.4*size_centered + 2*sst + 0.3*npp + 1.5*salinity + error,
         fishing_mortality = ifelse(size_centered < 0 & fished == 0, 
                                    10 + -0.1*size_centered,
                                    ifelse(size_centered < 0 & fished == 1,
                                           30 + 0.4*size_centered,
                                           ifelse(size_centered > 0 & fished == 0,
                                                  10 + -0.1*size_centered,
                                                  30 + 0.4*size_centered))),
         total_mortality = natural_mortality + fishing_mortality)

### Visualize mortality outcomes   
ggplot(crab_data) + 
  geom_point(aes(x = size_centered,
                 y = natural_mortality,
                 color = fished))

ggplot(crab_data) + 
  geom_point(aes(x = size_centered,
                 y = fishing_mortality,
                 color = fished))

ggplot(crab_data) +
  geom_point(aes(x = size_centered,
                 y = total_mortality,
                 color = fished))

### Visualize covariates
ggplot(crab_data) +
  geom_point(aes(x = size_centered, 
                 y = sst,
                 color = fished))

ggplot(crab_data) +
  geom_point(aes(x = size_centered, 
                 y = salinity,
                 color = fished))

ggplot(crab_data) +
  geom_point(aes(x = size_centered, 
                 y = npp,
                 color = fished))

Step 1: Determine if process of assigning treatment is rule-based

Example: Rule-based example with cut off: fishing size limits of crabs

In order to be legally harvest, crabs must be larger than 70mm. Crabs smaller than 70mm are not legal to harvest. Harvesting is thus rule-based, according to size. Here, we would probably expect mortality to decline with body size, but the harvest rule changes this relationship at the discontinuity.

Step 2: Determine if the design is fuzzy or sharp

Since we know that the program was applied based on a rule, we next want to figure out how strictly the rule was applied (e.g. was there a lot of illegal harvest of crabs that were too small? Were all crabs over 70mm harvested? ).The threshold was 70 mm for legal harvest — e.g., did people who caught crabs that scored 68 mm slip through cracks? The easiest way to check this is with a graph, and we can get exact numbers to verify with a table.

ggplot(crab_data, aes(x = size_centered, y = fishing_mortality, color = fished)) +
  # Make points small and semi-transparent since there are lots of them
  geom_point(size = 0.5, alpha = 0.5,
             position = position_jitter(width = 0, height = 0.25, seed = 1234)) +
  # Add vertical line
  geom_vline(xintercept = 0) +
  # Add labels
  labs(x = "Size (centered on 70 as cut-off)", y = "Fished or not") +
  # Turn off the color legend, since it's redundant
  guides(color = "none")

This discontinuity looks fuzzy rather than sharp We see some evidence of non-compliance around the size-based harvest rules. We will verify in Step 3.

Comparison of Fuzzy vs Sharp Discontinuities from Causal Inference: The MixTape by Cummingham

Step 3: Check for discontinuity in running variable around cutpoint

We next verify our conclusionss from the above visualization that the design is a fuzzy disconintuinity with a table examinging if there crabs under 70 mm harvested, and some over 70mm that weren’t.

crab_data  %>%
    group_by(fished, size_centered<= 0) %>%
summarize(count = n())

## `summarise()` has grouped output by 'fished'. You can override using the
## `.groups` argument.

## # A tibble: 4 × 3
## # Groups:   fished [2]
##   fished `size_centered <= 0` count
##    <dbl> <lgl>                <int>
## 1      0 FALSE                   79
## 2      0 TRUE                   421
## 3      1 FALSE                  441
## 4      1 TRUE                    59

Based on the table, we can conclude this is a fuzzy design becuase there are some crabs over the cut-off that were not fished, and some under that were fished.

Step 4: Check for discontinuity in outcome across running variable

Next, we need to see if any crabs self selected on either side of the size threshold; this seems unlikely. But, first, we’ll make a histogram of the running variable (size) and see if there are any big jumps around the threshold:

 ggplot(crab_data, aes(x = size_centered, fill = fished)) +
  geom_histogram(binwidth = 2, color = "white", boundary = 0) +
  geom_vline(xintercept = 0) +
 labs(x = "Size", y = "Count", fill = "Legal to fish")

## Warning: The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

Here it doesn’t look like there’s a jump around the cutoff. There’s a tiny visible difference between the height of the bars right before and right after the 70-mm sie threshold (centered at 0), but it seems to follow the general shape of the overall distribution.

Step 5: Measure the size of the effect

There’s a fuzzy discontinuity, but how big is it? And is it statistically significant?

Fuzzy RDD as IV

This is likely a fuzzy RDD set up: some crabs < 70mm are probably harvested illegally, and fishers are not catching every crab > 70mm. So the treatment assigned is not necessarily the treatment received. To estimate the effect of fishing on total crab mortality in a fuzzy RDD, we take a two stage least squares approach (using a the fuzzy RDD as an IV.

Recall from Session 12 that instruments let us isolate causal effects for just compliers: they let us find the complier average causal effect, or CACE (the effect of a treatment for subjects/units who comply with the experimental treatment assigned to their sample group).

In this case, the instrument is fairly easy and straightforward: we create a variable that indicates if someone is above or below the threshold. That’s all. This variable essentially measures what should have happened rather than what actually happened.

Surprisingly, it meets all the qualifications of an instrument too:

• Relevance (\(Z \rightarrow X\) and \(\operatorname{Cor}(Z, X) \neq 0\)): The cutoff causes access to fishing of crabs that leads to mortality.
• Exclusion (\(Z \rightarrow X \rightarrow Y\) and \(Z \nrightarrow Y\) and \(\operatorname{Cor}(Z, Y | X) = 0\)): The cutoff causes fishing mortality only through the harvest program.
• Exogeneity (\(U \nrightarrow Z\) and \(\operatorname{Cor}(Z, U) = 0\)): Unobserved confounders between the harvest program and fishing mortality are unrelated to the cutoff, since it may be biologically meaningful but the exact number is somewhat arbitrary.

Analyze fuzzy RDD

First we will create the IV from the cut-off. We have already centered the running variable (size) on 0, so now we just need to create an indicator variable if the size if above or below 0.

##NEED TO FINISHED

##        id fished      size      sst salinity          npp         error
## 1       1      0  41.84797 15.01488 5.545414 0.5122984664  3.3969839589
## 2       2      0  79.73803 10.72554 4.267921 0.8095724010  0.1253746350
## 3       3      0  55.19018 10.44435 3.126786 0.8203605369  4.3990486885
## 4       4      0  25.99801 10.57384 1.528624 0.7065953936  1.2974977910
## 5       5      0  16.93209 10.79003 3.185417 0.3172799677  0.5057971146
## 6       6      0  77.99594 10.96894 3.884679 0.9955174383  0.4577028855
## 7       7      0  75.78847 14.12099 8.459429 0.1811334651  0.3922578259
## 8       8      0  71.26553 14.02179 7.709277 0.3268148908  1.3296439782
## 9       9      0  14.34982 11.93525 4.715391 0.2017384777 -2.9739816639
## 10     10      0  22.80087 14.01309 7.572889 0.5894450329 -2.3019843168
## 11     11      0  42.60481 15.43312 1.602038 0.5618162802  3.2227520771
## 12     12      0  62.88149 15.71597 6.394025 0.8288963567 -2.1750029413
## 13     13      0  60.17699 10.35532 5.796374 0.4219403376  0.8822375574
## 14     14      0  32.59043 10.15416 3.818026 0.8700902204 -0.2491520273
## 15     15      0  51.26204 15.90615 4.762553 0.1247618941  2.7226801443
## 16     16      0  10.49994 13.33957 6.864297 0.6574287221  0.7003348420
## 17     17      0  42.11457 12.84864 9.428915 0.1309700655  0.6711096504
## 18     18      0  75.95654 14.13312 5.699696 0.7211235187  0.7889370497
## 19     19      0  40.02033 10.75790 2.766307 0.1889430520  1.5082758640
## 20     20      0  25.46802 14.32016 3.391951 0.7070721067 -0.3754883504
## 21     21      0  73.57829 11.65374 7.104121 0.2830847516  1.9474140003
## 22     22      0  73.77113 10.17380 1.659021 0.7839087658  1.4762403450
## 23     23      0  70.39111 10.72531 9.484125 0.1543507460  2.1068024106
## 24     24      0  48.51101 14.35260 8.366441 0.1691268147 -2.7909367857
## 25     25      0  24.51298 10.10666 2.818988 0.8754135838 -0.5422201475
## 26     26      0  77.88724 12.72474 6.710268 0.6226072919 -0.5719742850
## 27     27      0  65.55883 14.11271 7.756873 0.2401117554 -2.3161689689
## 28     28      0  67.41968 15.76721 6.684782 0.4999219819  3.0075259272
## 29     29      0  31.53491 11.77832 5.307226 0.7455336342 -1.9232422924
## 30     30      0  40.52941 12.73453 2.467462 0.7810508355  1.7487218861
## 31     31      0  19.45654 12.02799 9.415875 0.2963312902  0.9784903958
## 32     32      0  72.93853 10.68688 9.777817 0.0432374792  0.1140312712
## 33     33      0  62.42224 13.78415 4.352443 0.5107571867  0.6403206807
## 34     34      0  55.35832 12.60025 1.395540 0.3550621348  1.6030061242
## 35     35      0  66.14812 11.92191 5.977690 0.9392860658  0.0519689174
## 36     36      0  37.19295 13.58838 2.754159 0.1850668599  1.3820889683
## 37     37      0  62.96996 12.58675 8.341360 0.8649867503  2.6502074527
## 38     38      0  47.26075 10.51209 4.968321 0.7112351351  1.4034001158
## 39     39      0  15.21740 10.13269 3.673724 0.3645381115  0.2209358847
## 40     40      0  69.81422 13.23291 3.203782 0.9831388935  3.0807254861
## 41     41      0  32.60420 12.96117 1.522039 0.0617264931  0.1118555363
## 42     42      0  22.28027 14.43550 7.896019 0.1736047477  2.6013051240
## 43     43      0  16.39401 12.65178 5.314491 0.6231348314 -1.9095395440
## 44     44      0  26.70468 10.10301 4.972573 0.5215708176  0.6829802736
## 45     45      0  15.60613 14.31909 3.559101 0.4291872804 -2.7468414051
## 46     46      0  46.04189 15.84706 5.918764 0.1119348619  0.4560719601
## 47     47      0  29.03857 11.20811 2.234222 0.1252546546 -2.7555850172
## 48     48      0  12.56427 15.05049 4.436517 0.9253359330  1.3867785209
## 49     49      0  39.57454 11.12537 1.660280 0.5595281560 -1.2392024539
## 50     50      0  15.51346 11.31742 8.071734 0.9631643721  0.7381255821
## 51     51      0  48.38250 12.69948 8.017425 0.2620442947  0.8876103813
## 52     52      0  65.11413 15.76984 2.501628 0.0309782731 -0.3198516168
## 53     53      0  22.84824 15.15031 4.240319 0.0765342431  2.2165254546
## 54     54      0  64.20021 11.53364 2.128376 0.3658199674 -0.7852923782
## 55     55      0  14.50995 12.81946 3.799347 0.5117374037 -4.2985809929
## 56     56      0  18.21572 11.97044 5.108071 0.7054517686  2.5432584596
## 57     57      0  73.01384 11.20347 7.824564 0.1483750653  0.5144264427
## 58     58      0  79.01977 12.09899 1.066615 0.3810280049 -0.0683067826
## 59     59      0  28.77805 13.04654 9.829733 0.1768077554 -0.9312476481
## 60     60      0  35.24682 15.05166 4.142770 0.1817097727 -0.4606011425
## 61     61      0  70.20414 10.91182 7.219908 0.8815033613  2.4714938086
## 62     62      0  70.31827 13.46894 9.577780 0.7304476865  1.1759402509
## 63     63      0  57.06523 10.84315 3.655374 0.8600256352 -1.9380081427
## 64     64      0  72.91898 13.22309 8.883660 0.1794379631 -0.8443659858
## 65     65      0  38.67047 14.62388 3.753849 0.1743076388 -5.0651073159
## 66     66      0  69.97597 11.20178 1.063669 0.2996070071  1.5675415281
## 67     67      0  26.46307 11.63039 8.174687 0.7901809514 -1.1655098800
## 68     68      0  45.83037 10.30156 6.674546 0.5029937075 -0.0326504760
## 69     69      0  58.53935 10.55497 5.931420 0.0306283531 -0.1155761100
## 70     70      0  45.50775 13.11828 7.800584 0.0743867168 -2.0614441326
## 71     71      0  26.01266 12.91242 8.775044 0.3721621393 -0.8303960257
## 72     72      0  16.42100 11.29376 1.410725 0.2649603505 -2.4022119407
## 73     73      0  43.35972 15.23244 9.113410 0.8232880232 -3.2484080673
## 74     74      0  50.56978 15.68517 8.590039 0.7796957477  3.4820971738
## 75     75      0  65.27564 15.36784 3.018861 0.9696724361  1.7054502325
## 76     76      0  49.79546 15.89499 4.523502 0.5313015403 -0.0028462461
## 77     77      0  28.21531 10.98202 8.882294 0.9971313328 -2.4332206927
## 78     78      0  45.50296 12.67811 8.934493 0.8874159793  3.5915328205
## 79     79      0  22.60305 12.51546 6.139394 0.4119287438 -2.1188587402
## 80     80      0  56.39777 10.14164 1.298075 0.7278274598  0.5818998740
## 81     81      0  48.71824 12.92779 7.490425 0.6096635696  1.2272261547
## 82     82      0  26.68396 10.86137 5.355498 0.0612834888  2.0316798316
## 83     83      0  72.23963 12.44157 8.013368 0.8887657733 -0.6802550782
## 84     84      0  35.85515 12.88831 9.829259 0.8944283871 -2.2706815212
## 85     85      0  79.76453 12.60060 6.432885 0.9706627983 -3.1244579010
## 86     86      0  14.09337 12.05203 7.920201 0.5212248899  0.0667089679
## 87     87      0  33.37735 13.46307 1.760967 0.8986572046  0.9253533551
## 88     88      0  57.60634 13.89445 8.371074 0.9768107254 -0.4340780850
## 89     89      0  10.83747 10.21515 8.162783 0.4039448590  1.6791313729
## 90     90      0  24.49206 14.27505 1.577690 0.0234826030  0.9076616032
## 91     91      0  79.32137 13.17095 3.515679 0.9608223382  0.5264126248
## 92     92      0  30.44873 11.21197 6.909163 0.5110034277 -2.7297933247
## 93     93      0  33.52545 13.03120 1.188815 0.3936737247 -2.9302804428
## 94     94      0  78.79096 13.29567 9.266841 0.9073055424  0.7799769576
## 95     95      0  46.38155 12.87570 8.756405 0.3437323764 -1.4345715721
## 96     96      0  26.99989 14.09412 8.873921 0.2134562279 -1.6746520175
## 97     97      0  55.06387 12.80434 2.877051 0.7619143345 -2.9313977920
## 98     98      0  25.31338 15.31941 8.280588 0.2213303880  1.0348317305
## 99     99      0  67.39879 13.16029 3.749055 0.7366472881 -1.5175630351
## 100   100      0  49.89301 15.71041 8.294970 0.1869371529 -0.4131680964
## 101   101      0  38.66793 10.43607 4.144904 0.0392171801 -3.1838099014
## 102   102      0  14.68882 11.80734 6.164031 0.3123323028  0.3349038619
## 103   103      0  29.87938 14.65559 8.917850 0.9684240224  0.7865166947
## 104   104      0  25.41085 11.06034 4.393528 0.5109950609 -0.1353561202
## 105   105      0  15.57580 13.38560 2.307871 0.9150218209 -1.0580629055
## 106   106      0  47.39121 14.65672 6.960592 0.4558633366  2.4267994039
## 107   107      0  40.48732 14.71303 6.670824 0.5734539097  1.7028136421
## 108   108      0  36.26677 12.71401 2.170721 0.8508319431 -0.7982042586
## 109   109      0  13.34889 14.19463 6.777333 0.6029144635  1.7440143467
## 110   110      0  61.65646 13.21078 9.457444 0.9750003896  4.2425261966
## 111   111      0  28.79088 14.87107 2.544236 0.9093731826 -0.3275293352
## 112   112      0  10.06158 15.91344 4.996650 0.6399102909  1.1945664792
## 113   113      0  58.33446 12.34006 5.220775 0.6617895542  1.3830643760
## 114   114      0  34.10013 10.92581 2.290369 0.4201782672 -3.5480279999
## 115   115      0  57.30338 11.37179 6.177431 0.4678367155  1.1750156527
## 116   116      0  40.81362 13.88085 8.247046 0.9030558849 -3.8594159620
## 117   117      0  77.12404 15.20979 3.055968 0.7234343733 -0.8245310309
## 118   118      0  65.13657 15.48676 3.381153 0.9859646019  1.9353056903
## 119   119      0  73.22936 15.07964 1.471651 0.2880695490  0.5572993473
## 120   120      0  10.40575 11.91318 6.183794 0.4355266048 -2.6441643647
## 121   121      0  32.31772 10.79653 6.569972 0.7499470473  0.3139303127
## 122   122      0  57.41269 15.15925 5.322542 0.7455334389  1.7557478129
## 123   123      0  76.82869 11.16442 3.458440 0.5644706700 -0.0530984827
## 124   124      0  70.77481 13.85297 4.055676 0.7499118163  1.6598986400
## 125   125      0  38.63745 12.37969 4.872155 0.7665744072 -0.5987688536
## 126   126      0  11.02867 12.31414 2.113859 0.1527790776 -2.7719897802
## 127   127      0  50.34350 12.07887 1.184923 0.0673992594  1.0325604849
## 128   128      0  37.84255 12.84449 5.496648 0.6703295272 -0.1850263852
## 129   129      0  74.22559 11.71944 3.843540 0.0811288576 -0.4845985592
## 130   130      0  37.76976 12.77118 9.410009 0.9694322716  1.0104942167
## 131   131      0  33.71929 14.01138 9.654346 0.7572716225  0.0903822824
## 132   132      0  42.79985 10.70880 1.740517 0.9503490352 -2.3317726547
## 133   133      0  61.23944 10.24088 1.122617 0.2837087386 -0.5176609740
## 134   134      0  25.23067 13.44719 7.364621 0.7485409766 -0.3495062834
## 135   135      0  76.52360 15.83878 2.097535 0.5798271280  2.1719130269
## 136   136      0  28.28269 14.78496 8.763782 0.7496547576 -0.2857654708
## 137   137      0  12.21055 10.02816 2.486694 0.4247822030  0.8581857994
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## 368   368      0  51.20533 12.62080 8.450279 0.1987620038  1.5517975807
## 369   369      0  45.52415 11.50524 9.380893 0.8883235457 -3.6857389303
## 370   370      0  62.28094 13.80141 7.363388 0.8445861498  0.9411404160
## 371   371      0  72.37168 10.95888 8.211240 0.2480726044  1.9287283594
## 372   372      0  17.37636 10.98613 2.970641 0.4951685357  0.4591266746
## 373   373      0  75.03401 11.81503 2.181171 0.8902233960 -0.1881232789
## 374   374      0  17.63042 11.59854 2.258187 0.5052518160  0.6466011946
## 375   375      0  36.91635 11.65129 9.489200 0.8789280518 -1.5507735326
## 376   376      0  28.63814 11.60892 3.042836 0.1472055230  0.3760564573
## 377   377      0  20.40791 11.51432 8.311235 0.8184613150  0.5071615055
## 378   378      0  76.64363 14.70663 8.850232 0.6200305705  0.0149493172
## 379   379      0  61.49750 12.19849 8.515360 0.0893945014 -1.2695697613
## 380   380      0  68.92625 14.50548 3.347399 0.0037886577 -1.9682785540
## 381   381      0  66.26531 14.35041 1.334380 0.1115272150 -2.0325799228
## 382   382      0  68.19234 14.70669 1.174327 0.3624465184 -0.8119884968
## 383   383      0  10.58423 15.79517 2.649775 0.4491898392  0.6471760087
## 384   384      0  79.23948 14.82336 3.319169 0.4846168510  1.5044579007
## 385   385      0  13.38721 15.43744 8.702756 0.9717950984 -2.1125424945
## 386   386      0  26.61996 13.85861 1.294941 0.5023312098  1.4004275332
## 387   387      0  39.64902 14.17389 4.480814 0.7588781090 -1.3246890084
## 388   388      0  76.14997 14.76367 4.454225 0.2305689673 -1.3612536987
## 389   389      0  61.83502 10.43479 3.288955 0.6757032436  2.3390214673
## 390   390      0  54.14373 12.97125 2.860543 0.9583313446  1.1433997103
## 391   391      0  77.57915 10.10239 2.408587 0.1602448486  0.7325751766
## 392   392      0  29.36386 10.82168 7.787122 0.5837937500  0.7825640144
## 393   393      0  59.87335 13.61023 8.604789 0.6787609435 -2.3575681957
## 394   394      0  18.07021 13.35824 5.075400 0.5543806516  0.7973874079
## 395   395      0  33.17805 10.77846 6.041984 0.9512208116  0.9672301877
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## 397   397      0  39.25472 14.56819 4.824601 0.3742196038 -1.5981793281
## 398   398      0  28.67276 15.25601 6.608124 0.1947518443 -0.8537534697
## 399   399      0  52.99094 11.92965 7.332993 0.9611510970  2.8425570687
## 400   400      0  65.85638 12.96956 3.680195 0.2889470665  3.1259419972
## 401   401      0  62.62337 11.74092 3.780227 0.1507460603  2.1919604681
## 402   402      0  75.05604 11.85906 6.488490 0.0226344294  1.5098762334
## 403   403      0  34.53302 14.97581 2.857427 0.6196427189 -1.2026305368
## 404   404      0  29.24367 10.97021 5.532371 0.4944418133  1.1635336483
## 405   405      0  74.63395 11.05575 9.595956 0.4585071071  2.2839463807
## 406   406      0  30.33718 12.53621 7.148493 0.6497489095 -2.0327340758
## 407   407      0  20.81346 11.71648 9.061133 0.6548257479 -0.8714251644
## 408   408      0  28.76802 11.11741 8.841816 0.8452985501  0.6034956509
## 409   409      0  13.81760 12.24872 3.335317 0.1477635994 -4.1952850854
## 410   410      0  76.30012 13.75218 5.878224 0.0351953523 -1.5945684132
## 411   411      0  40.61717 11.58233 2.081942 0.1413649926 -0.1268339458
## 412   412      0  16.90014 10.83425 1.921788 0.8445973911 -0.2703690668
## 413   413      0  17.21898 15.34525 6.990534 0.6432073771  0.1314030806
## 414   414      0  74.39063 10.68710 6.736115 0.7448168448 -1.3693156373
## 415   415      0  71.80266 12.55282 8.982233 0.0608962271 -2.0096909042
## 416   416      0  42.93401 13.54857 8.335447 0.5636339784  0.2729884577
## 417   417      0  78.41527 13.56829 7.512674 0.9311568860 -1.0833220899
## 418   418      0  56.63197 15.76110 5.285695 0.4018990365 -1.3747385063
## 419   419      0  42.00630 10.93876 7.056109 0.2981208579  0.3444406430
## 420   420      0  65.45635 14.30321 6.168867 0.4961668809 -2.7495037885
## 421   421      0  74.93580 15.93456 4.023580 0.1967162734  0.3668013375
## 422   422      0  19.80601 15.54653 3.770793 0.5749203113 -0.0380405135
## 423   423      0  54.85718 14.71216 1.059221 0.7433558586 -2.4176733852
## 424   424      0  44.09390 15.35116 6.554568 0.0041635716 -0.2968673417
## 425   425      0  60.12215 15.70613 8.726366 0.6796121059 -2.4849569529
## 426   426      0  52.62165 14.49167 9.903337 0.8250616163  3.0293648107
## 427   427      0  65.45816 15.66282 3.083509 0.1729694637  1.1701675087
## 428   428      0  74.62324 14.27530 1.048396 0.5900472007  7.2121248190
## 429   429      0  64.05148 15.47070 8.355980 0.9967813599  2.4490258621
## 430   430      0  60.14832 13.03795 2.038228 0.8966289018  1.2269767135
## 431   431      0  41.06760 13.25776 5.586159 0.7707323357 -1.8698191655
## 432   432      0  21.17524 15.93643 4.053686 0.0898875613 -1.6162210797
## 433   433      0  19.39057 14.55736 7.376965 0.0997058915  0.8118020882
## 434   434      0  66.40170 11.60275 6.560765 0.9926928950  0.6406634879
## 435   435      0  35.55058 11.13460 6.128547 0.9752784087  0.8591499506
## 436   436      0  74.45650 14.62986 2.225857 0.6686680201  2.1569672305
## 437   437      0  75.07443 13.96170 1.477113 0.3937187307 -0.2825536193
## 438   438      0  55.77173 14.66111 3.301127 0.9772212701 -1.3624220059
## 439   439      0  45.33560 14.12431 2.000664 0.1370297200  0.6065689448
## 440   440      0  56.17164 12.07809 6.459881 0.5162824432 -0.7483572420
## 441   441      0  43.75993 12.66633 7.775599 0.3970756007  0.3580526783
## 442   442      0  49.68636 10.79552 3.368768 0.8308092637 -0.0388933922
## 443   443      0  60.94715 12.97481 9.730456 0.6021083628 -2.9711879588
## 444   444      0  76.87973 12.51879 7.363903 0.3398860849 -4.1295072207
## 445   445      0  21.80218 13.25431 4.330574 0.9273858250 -1.2551533636
## 446   446      0  46.87964 10.39933 3.144543 0.8698163386 -0.9710742953
## 447   447      0  30.20317 14.54391 4.939594 0.8982378046 -0.1637083344
## 448   448      0  59.79609 11.55675 4.586748 0.4634068774 -0.3843512451
## 449   449      0  68.90790 15.59354 6.781255 0.2159462769 -1.2368586133
## 450   450      0  73.31741 11.93059 6.378449 0.9466458680 -1.3123583848
## 451   451      0  32.02334 12.02544 7.072739 0.5304137829 -1.8051926603
## 452   452      0  57.25424 15.68416 2.350769 0.2741397829 -0.0079076274
## 453   453      0  50.56297 15.64910 4.484043 0.8429498901 -3.7051714452
## 454   454      0  52.31877 12.59731 9.644301 0.9617204498 -1.8339641199
## 455   455      0  32.71982 12.19022 9.625441 0.3475991657 -2.0952175663
## 456   456      0  49.17960 10.16150 5.164256 0.6551162121  2.0294600121
## 457   457      0  24.71140 14.72911 4.195559 0.1609277690  0.6806588270
## 458   458      0  10.90848 10.32208 2.011801 0.4738924245  0.1818382999
## 459   459      0  27.83821 13.72928 7.487488 0.8204968611 -3.2920896101
## 460   460      0  44.40471 11.90589 5.126837 0.5659135433 -1.6608637528
## 461   461      0  65.47207 12.86583 4.872788 0.8950806365  0.6419738748
## 462   462      0  75.86325 10.14427 2.051659 0.3737650225 -2.9365171080
## 463   463      0  16.83136 12.49160 9.706837 0.1146005511  1.8143734212
## 464   464      0  51.39573 12.00589 3.180673 0.9345218593  2.0625309267
## 465   465      0  28.26352 11.92784 7.773125 0.1256269335  2.3360033106
## 466   466      0  73.01473 15.04627 8.020581 0.7835060761 -2.9105275662
## 467   467      0  78.93526 15.59652 7.535608 0.9914062128 -0.5982757757
## 468   468      0  17.68080 11.14500 7.129912 0.9864133135 -0.5775421529
## 469   469      0  76.55174 11.52552 6.634586 0.2214863393 -4.0643515837
## 470   470      0  54.77879 10.00288 5.592868 0.5886946707  4.1220885865
## 471   471      0  62.46771 14.25536 4.331537 0.2695323895 -0.8923735243
## 472   472      0  20.01843 14.19031 8.092329 0.4363202138 -0.7204197007
## 473   473      0  54.96714 13.56013 8.411986 0.0003411265  0.1091861318
## 474   474      0  70.07682 12.81629 6.842217 0.3598351909  0.3659407057
## 475   475      0  43.51918 11.42335 1.292800 0.6596575389  0.7966076530
## 476   476      0  25.62279 15.43585 3.207972 0.1859156305  1.1288945075
## 477   477      0  16.28907 10.84736 7.090749 0.5313337154 -1.4055115025
## 478   478      0  44.25334 10.03680 1.160673 0.3142974034 -1.7580277527
## 479   479      0  20.86461 14.91444 4.555649 0.9801418099 -1.8546614081
## 480   480      0  11.87823 15.56351 3.401203 0.2837930175 -4.4868228982
## 481   481      0  33.15158 10.40613 4.147724 0.5786049184  1.0228941759
## 482   482      0  20.88009 15.50282 2.571700 0.0181206265 -1.1077485088
## 483   483      0  59.45803 10.81515 3.028410 0.7163714934 -0.2664437190
## 484   484      0  13.71196 10.89003 4.996990 0.3865434739  0.4793675262
## 485   485      0  41.00238 10.59809 2.623292 0.0510326747 -1.2309297984
## 486   486      0  70.79542 13.70722 5.301262 0.5883173903  0.4384610948
## 487   487      0  13.76568 15.50190 8.128257 0.7313689906 -1.9386659300
## 488   488      0  27.09578 11.64710 8.841020 0.7625001562  0.6035483622
## 489   489      0  20.67865 11.13734 5.559085 0.1945629921 -1.7174439049
## 490   490      0  58.46395 11.39980 9.888942 0.5747248929  0.8846338820
## 491   491      0  59.69128 14.69430 9.770612 0.7632682808 -0.7060349601
## 492   492      0  27.57357 13.63639 3.145035 0.4323440520  2.3714450780
## 493   493      0  51.88301 12.79097 3.541861 0.4758024579  0.8024162921
## 494   494      0  16.67719 14.26818 6.642059 0.0379647361  0.2760082018
## 495   495      0  45.13847 15.24529 6.825422 0.3084082138  3.0426899408
## 496   496      0  40.22571 10.05576 4.078273 0.7508620680  0.7123419172
## 497   497      0  77.96816 13.01885 9.885625 0.2146871290 -1.1354544050
## 498   498      0  73.55536 11.36350 8.492139 0.0485513110  0.0175468269
## 499   499      0  62.46098 12.63002 4.249147 0.8886069439 -1.4824810037
## 500   500      0  53.24974 13.62109 6.393217 0.1107497569  0.7517708133
## 501   501      1  71.09375 13.73441 3.224278 0.3811226401 -1.1277813367
## 502   502      1 126.32809 15.37795 9.350874 0.8336211659 -1.0800118494
## 503   503      1  60.70570 13.78599 9.442488 0.0485620485 -1.1495165868
## 504   504      1 111.51297 10.29176 4.928723 0.0173637520  1.6524307251
## 505   505      1  99.72688 11.99874 7.600097 0.0810297427 -0.4271348934
## 506   506      1 126.47106 10.69722 4.242467 0.9216875178 -0.9124521204
## 507   507      1 107.62346 11.44205 9.726791 0.5173406063 -1.6721363929
## 508   508      1  98.77177 12.48195 8.352858 0.4487846021 -2.5797907162
## 509   509      1  65.16515 15.05760 6.711653 0.1410812661  0.2326779029
## 510   510      1  77.10813 14.07526 6.088693 0.8098178387 -1.4209588861
## 511   511      1  90.69457 15.28851 5.838034 0.5742706414 -1.2770490721
## 512   512      1  81.12945 10.67494 3.415427 0.8947175797  0.6566267171
## 513   513      1 101.56572 14.99493 9.541247 0.1076762353  1.2859536159
## 514   514      1  98.35121 13.40496 1.881698 0.8619494471 -0.1146414082
## 515   515      1 105.74416 12.69122 2.864491 0.9931341421  0.4419941758
## 516   516      1 126.65594 15.12601 9.959940 0.4510069021  1.2504389498
## 517   517      1  88.09558 10.03126 7.264234 0.0960929722 -0.4829587033
## 518   518      1  90.82187 14.84416 2.530271 0.5234884126  4.0710212015
## 519   519      1 110.09624 11.96924 4.070851 0.1205681250  0.2777353969
## 520   520      1 122.90750 10.83117 9.156646 0.8867086505 -1.7720421094
## 521   521      1  83.56281 10.19737 6.471340 0.3720571841 -1.3236686607
## 522   522      1 105.39671 11.67692 5.469728 0.6124727714 -0.4078010704
## 523   523      1 124.72976 15.58337 7.809839 0.8692817960  2.5207817851
## 524   524      1 121.64639 11.94480 8.855619 0.3873691149 -2.9713829760
## 525   525      1  78.16460 14.95888 4.200646 0.2523658446 -0.8843918988
## 526   526      1  77.50127 12.40077 9.573604 0.5314695146  0.5287123658
## 527   527      1  81.66920 15.17542 1.421705 0.9759295133  0.2685532603
## 528   528      1  99.07612 11.38454 5.099804 0.3265321103  0.9626051063
## 529   529      1  89.99200 11.71025 8.268850 0.9289248106 -2.7824132262
## 530   530      1  87.86177 13.75883 6.309825 0.6556658014  1.0095248578
## 531   531      1 112.86845 13.62924 4.222356 0.5162548004 -2.1152462630
## 532   532      1  78.92798 13.34869 1.042287 0.2604255844  2.0960120682
## 533   533      1  83.26196 10.73944 2.299465 0.3967446918 -0.7314765868
## 534   534      1 119.68931 11.96477 2.061999 0.7454329457  0.7452390672
## 535   535      1 122.96620 14.95138 1.396510 0.3242380647  4.0801760678
## 536   536      1 113.31714 14.56473 9.948150 0.5355195485 -0.0003730287
## 537   537      1 124.65899 12.12800 2.558927 0.2557019340  0.2565894672
## 538   538      1 107.74554 14.46411 1.666547 0.7216503194  0.1279647112
## 539   539      1  63.08914 15.71141 7.483712 0.4272211366  0.2487158491
## 540   540      1  64.25090 10.36897 9.103643 0.3252407066 -3.5686421788
## 541   541      1 126.52824 14.88484 8.588881 0.9679650776  1.0598105852
## 542   542      1 110.30468 10.90103 9.042107 0.4297251031 -1.8461421821
## 543   543      1 102.70844 14.04437 8.290922 0.2720003361  1.1061963104
## 544   544      1  76.82632 10.21477 3.579597 0.6440374067  0.4717897051
## 545   545      1 117.89912 13.98916 9.537609 0.5797165108 -2.5611940841
## 546   546      1  62.72415 15.72086 4.476041 0.0923021757 -0.5645884724
## 547   547      1 120.72582 13.57795 6.426918 0.9414535225  0.5790043059
## 548   548      1  61.94241 12.69431 8.807178 0.0808953515  0.5464023607
## 549   549      1 101.37838 14.22506 7.837434 0.1470729166  0.9914475961
## 550   550      1 126.11002 11.10884 8.412291 0.5867140444  0.4016734988
## 551   551      1  82.27595 13.94485 5.521372 0.4820108393 -3.9801003541
## 552   552      1 127.51614 11.26688 6.821205 0.0976113854  0.6344551657
## 553   553      1  88.80640 10.08139 1.568284 0.8277146965  3.5057969212
## 554   554      1  81.85504 14.40172 9.394055 0.9935439401 -1.6133422251
## 555   555      1 110.59072 15.44455 5.905034 0.7245926908 -1.1422829725
## 556   556      1  77.84199 12.28347 5.401996 0.4055178768  0.2939166806
## 557   557      1 104.98405 11.43773 5.747301 0.4479928722  3.5246118323
## 558   558      1  98.24844 14.57829 7.128312 0.6596412850 -0.9155837244
## 559   559      1  76.70357 12.98858 3.968288 0.6551032648 -2.3418918831
## 560   560      1  92.85246 14.47199 6.241274 0.6268161251 -3.1686730524
## 561   561      1  65.24394 13.95940 1.233960 0.9402681233 -2.6937091899
## 562   562      1  80.85783 12.51497 5.959051 0.6813228996  2.4595293331
## 563   563      1 111.17503 13.74410 1.618870 0.9198924657 -2.9422017169
## 564   564      1 107.20313 11.24045 7.284155 0.8554095225 -0.4774261729
## 565   565      1  62.07709 10.65758 8.713307 0.7329774878  2.2212352093
## 566   566      1 125.97037 13.53590 5.255857 0.7950108610  0.0233511323
## 567   567      1 119.63912 13.59427 3.898774 0.0546908062  3.0608445056
## 568   568      1 128.81516 15.72543 9.625129 0.3064621857  0.6514285762
## 569   569      1  86.85478 13.30193 9.673018 0.1163828149 -0.1826875431
## 570   570      1  60.41396 13.21590 3.933433 0.6578448047 -0.3677385493
## 571   571      1  72.58332 11.08750 5.450847 0.8892998572  0.9995442162
## 572   572      1  68.99734 13.90499 1.259839 0.7746068556  4.0109144291
## 573   573      1 114.54196 12.16096 1.318244 0.2454774850  1.0883967457
## 574   574      1  88.81161 14.69879 1.912856 0.9838066960  0.2162441426
## 575   575      1  65.08443 11.28499 6.063479 0.2250178438 -2.1948531830
## 576   576      1 125.85078 15.67139 8.121180 0.9676186277  2.5025869106
## 577   577      1 127.97222 13.01875 9.981692 0.9479246957 -0.1670800841
## 578   578      1  92.53388 12.90727 6.775118 0.6409801200 -1.5661874921
## 579   579      1 126.76222 14.30024 4.114406 0.3227941853 -1.9315885164
## 580   580      1 114.45424 12.69667 8.943676 0.4509644352 -2.6162277915
## 581   581      1 105.89943 12.95519 4.775822 0.8744527786  1.7481987635
## 582   582      1 113.98057 11.19931 1.756662 0.4741021350 -1.0757211357
## 583   583      1 102.06807 13.48389 6.514471 0.5019704988 -1.6963186372
## 584   584      1 103.65743 11.00417 5.840404 0.7209678893  0.8265054281
## 585   585      1  77.87212 13.95456 7.483491 0.2110914073  1.1781853858
## 586   586      1 123.55098 14.73105 1.423518 0.2947722888 -1.5549017369
## 587   587      1  65.67367 10.22679 3.415892 0.6387341635  0.6146724349
## 588   588      1  78.44929 12.48415 9.808110 0.9299567665 -1.0666057764
## 589   589      1 113.52809 14.42400 2.927018 0.8122926936  2.7639029451
## 590   590      1 129.11221 10.83874 9.282479 0.4221205253 -2.2015218435
## 591   591      1  71.90160 14.60120 2.608383 0.5024504336  2.7763084618
## 592   592      1 120.04748 12.16184 5.467234 0.9282543513 -0.0950758972
## 593   593      1  79.87857 10.46516 1.523942 0.9885493203  0.8585133182
## 594   594      1 113.91810 12.83868 6.091970 0.1090847554  0.3999940532
## 595   595      1  68.22396 10.47893 5.898581 0.9876280774 -0.4097475938
## 596   596      1  79.86288 15.53500 4.166497 0.1678521822  3.2820979483
## 597   597      1  61.19947 13.47359 7.010138 0.6176363213 -0.6985686881
## 598   598      1  73.41503 10.15375 5.939332 0.4154718057 -4.1694487910
## 599   599      1 127.31210 15.17727 9.386552 0.2197215504  3.4722830531
## 600   600      1  82.04856 12.17720 4.129320 0.7828368268 -1.9322223834
## 601   601      1 122.89147 10.22953 3.884780 0.7611336571 -3.2469200740
## 602   602      1  90.70649 14.76079 3.424879 0.1978355844  1.3707186597
## 603   603      1  62.44121 14.92982 7.541224 0.9821627806 -1.8182524220
## 604   604      1  73.98503 14.12738 8.255691 0.6073207150 -0.5640998663
## 605   605      1 102.80856 13.61256 3.840115 0.6271756294  0.4299693751
## 606   606      1  78.23796 11.99844 5.764991 0.8748706898  1.6962616682
## 607   607      1  85.86202 13.32467 6.689241 0.8628359661 -3.4729835705
## 608   608      1 124.16979 11.95920 2.240594 0.8901314882 -0.4951265332
## 609   609      1  99.03590 11.46940 4.952784 0.1583011772 -4.6749685926
## 610   610      1  91.87050 14.04735 1.616860 0.9132679559  1.0297170118
## 611   611      1 128.95299 14.19806 2.588168 0.7595219722 -0.0317307380
## 612   612      1  60.63628 13.11654 3.702142 0.0089792863  0.0848083537
## 613   613      1  66.20274 12.74622 3.966828 0.7719678674  0.2389427859
## 614   614      1  81.92418 15.00601 7.560038 0.1737857335  1.1217697746
## 615   615      1 103.22342 10.19367 2.872438 0.6535111961  0.4761029831
## 616   616      1 113.32461 15.52728 6.073652 0.1819786888 -0.0774222570
## 617   617      1 113.66937 12.33438 4.289158 0.5588189340 -0.3725501409
## 618   618      1  86.98113 11.36934 2.144613 0.7425258609 -1.7684092809
## 619   619      1 118.43302 14.89077 4.839411 0.2663916922  2.0304083114
## 620   620      1  75.67531 15.99457 4.614154 0.1274022085 -0.6376629291
## 621   621      1  84.73703 11.40081 5.071217 0.9775445643  0.5091754800
## 622   622      1  97.37698 10.72696 4.573730 0.7640859266 -0.1560813318
## 623   623      1 129.26840 11.13548 7.992133 0.6951857314 -2.0054916665
## 624   624      1 104.62107 11.76567 9.085490 0.8324761062  1.2290657377
## 625   625      1  91.76325 10.95237 1.657323 0.8555798288 -2.9648819466
## 626   626      1  75.21960 14.93207 8.367494 0.7970403242 -2.2114269508
## 627   627      1 103.19470 11.12863 7.597325 0.4762284488  2.8579739902
## 628   628      1  71.14733 12.96985 3.799667 0.7595792820 -1.0105729989
## 629   629      1 127.56881 13.00589 2.371670 0.4974276884  0.6353450579
## 630   630      1  87.26262 13.02898 6.455686 0.1869858657 -0.6331183873
## 631   631      1  64.41432 13.30734 6.355570 0.4928022348 -1.0048365036
## 632   632      1 128.16355 10.15181 2.262575 0.0040129796  0.1338179441
## 633   633      1  63.61155 15.27585 1.370792 0.2512427124  3.1404716553
## 634   634      1  90.95011 12.08355 2.346858 0.6747299551  1.7406924674
## 635   635      1 117.89657 12.79735 9.692960 0.2627696262  0.4307791789
## 636   636      1  77.68609 15.41417 5.932440 0.8888018322  0.5169252500
## 637   637      1  95.03188 13.17728 3.822366 0.8555523343  0.5613992638
## 638   638      1  72.11967 13.57216 1.644029 0.0046312015 -3.7798527414
## 639   639      1  86.57895 10.92480 3.482500 0.6735297786 -2.3836786467
## 640   640      1 127.97412 12.50735 5.501585 0.5503835045 -3.5960453774
## 641   641      1 112.30355 14.11468 7.211773 0.2090930198 -2.5031554201
## 642   642      1  73.90254 11.41225 4.301113 0.3099311965 -1.4031644349
## 643   643      1 103.63438 10.67842 4.988927 0.5553910141 -0.1960718462
## 644   644      1 117.53617 15.20117 9.712668 0.3215704684 -5.6958455510
## 645   645      1  73.16716 13.06031 4.539068 0.6787757871 -1.1394611760
## 646   646      1  93.22770 14.38620 1.577585 0.8903287775 -1.1277282325
## 647   647      1  68.06833 14.66192 9.944449 0.1355676162  1.5299553866
## 648   648      1  94.14657 15.66798 8.574401 0.3348297004 -2.1923807064
## 649   649      1  75.46969 12.48481 9.564024 0.4361352012 -1.7867926767
## 650   650      1 117.73631 15.64146 2.399623 0.1520993349 -0.3466060378
## 651   651      1  78.25068 12.63499 4.139099 0.1738081744 -1.7959963858
## 652   652      1 114.59001 12.85813 2.261998 0.5716521444 -1.5400911379
## 653   653      1 101.99263 10.22411 3.947036 0.3560642302  0.8034361595
## 654   654      1 114.07889 10.97910 4.175316 0.8196217325 -2.3490228909
## 655   655      1 115.39233 11.72523 4.585496 0.8671832110 -2.7482801129
## 656   656      1 125.45707 13.12836 7.656521 0.3827806769  2.1630526092
## 657   657      1  88.14015 11.99829 4.389754 0.1456623056 -0.7280714006
## 658   658      1  73.37135 14.39776 1.684903 0.7700847795  0.8638167765
## 659   659      1  92.05532 15.93471 1.474193 0.2374253576  0.8894896648
## 660   660      1 112.74128 12.03237 2.272816 0.6034437628 -0.6019003992
## 661   661      1 118.87836 10.90377 2.162548 0.7938392861 -2.4776662958
## 662   662      1 101.77763 15.74620 2.774411 0.6678117164 -1.1374923837
## 663   663      1  86.73386 12.65505 9.412207 0.9229583535  4.7445116686
## 664   664      1  94.59739 13.47288 8.898343 0.5525978496 -0.0657536253
## 665   665      1 109.83213 11.41326 9.449637 0.2220031919 -1.7328901640
## 666   666      1 128.67814 13.52263 3.474435 0.7584428091  2.1185061855
## 667   667      1 121.58862 14.96588 2.239605 0.1283352373 -3.2514737019
## 668   668      1 125.49574 14.45059 1.366447 0.6841582113  2.3641220385
## 669   669      1 106.04468 12.67405 1.914319 0.7617197733  1.8735693874
## 670   670      1  90.82412 14.45647 9.105721 0.5588631153 -0.8343830565
## 671   671      1 117.36964 13.02610 4.513783 0.1763611413 -1.1878926340
## 672   672      1  75.27841 13.26637 7.420659 0.7203251712  2.1677600223
## 673   673      1 128.87775 11.82290 5.076439 0.8224302437  1.1882196270
## 674   674      1 104.42799 14.39172 1.723633 0.2770354059  1.9049068251
## 675   675      1  60.73863 14.19311 9.279399 0.0484020461  0.9046795473
## 676   676      1  84.03755 12.66196 9.512154 0.8787558530  1.0585488745
## 677   677      1  84.66854 10.89828 8.150108 0.4813408155 -3.4081121416
## 678   678      1 117.80104 13.44284 6.950090 0.7553483481  1.4504276857
## 679   679      1  60.74533 15.78355 3.881187 0.9935191753  1.0605579453
## 680   680      1  81.67254 13.44599 2.679285 0.7830495222 -3.5098830728
## 681   681      1  62.25209 15.21333 5.400361 0.4150345083  0.6358955431
## 682   682      1 118.30088 12.87195 7.062045 0.6235786092  1.2465327176
## 683   683      1  91.88426 10.35207 4.859515 0.7273605629 -2.2387670011
## 684   684      1  95.00512 15.04798 4.396901 0.1512960664 -0.8497282446
## 685   685      1  77.37011 15.46457 2.980307 0.5207782558  0.7784986831
## 686   686      1  64.31016 14.50060 4.610657 0.9018138973 -1.1501567462
## 687   687      1  85.35310 13.78461 4.549883 0.3497820836 -0.4250373844
## 688   688      1 101.74763 13.44986 2.673678 0.3343934503 -1.6282804978
## 689   689      1  90.52439 11.39923 5.035895 0.2047378493 -0.7053422182
## 690   690      1  70.64950 13.74313 4.367925 0.1999019468  0.1797921260
## 691   691      1 105.67126 10.84119 2.562103 0.2277797519  0.8307588598
## 692   692      1  90.75400 12.85485 5.042407 0.0904976553  0.8012975068
## 693   693      1  75.62299 10.54072 8.502436 0.3807463341 -0.0727553636
## 694   694      1  66.16380 13.58043 3.939569 0.3377748833  1.5956781790
## 695   695      1  99.09358 11.57802 2.751146 0.3273471666 -1.3484343314
## 696   696      1  95.99445 15.49400 3.214185 0.2579937803  0.5544009581
## 697   697      1 108.42121 10.15390 5.728883 0.7976588311  0.2183880883
## 698   698      1  74.58613 15.43237 2.094772 0.0681968592  0.2940315100
## 699   699      1  96.06878 12.12093 9.098548 0.8341346914 -2.2595392425
## 700   700      1  77.97835 15.12533 9.394104 0.7797295759  0.8426044301
## 701   701      1 120.96790 15.06921 4.775708 0.4939177795  1.3452776595
## 702   702      1  83.33325 15.30763 4.530343 0.4847417087  0.2956032912
## 703   703      1  91.90062 10.51839 8.027868 0.0605730237 -2.2269745061
## 704   704      1 126.57396 11.05689 4.110621 0.8503145932  3.8479837099
## 705   705      1  81.21869 15.59641 2.621131 0.7973399092  0.3021538351
## 706   706      1 123.14577 10.47015 6.986632 0.7746588963  1.9942552137
## 707   707      1  72.72763 11.49872 8.294926 0.9113698122 -1.2412466843
## 708   708      1 108.14784 13.70138 5.687487 0.0435425350  1.1805913518
## 709   709      1  93.04247 10.94106 3.971770 0.2491262159 -3.3234002817
## 710   710      1  83.73825 13.79641 1.493518 0.8713187645  0.3052080728
## 711   711      1  83.17460 13.15491 3.171608 0.9821822916  0.7061510303
## 712   712      1  91.80312 15.20661 8.763561 0.2077412487  2.8074845155
## 713   713      1 124.48839 10.91239 7.562919 0.9343241509  0.5440337334
## 714   714      1 115.81172 11.59413 8.991550 0.4305132201 -2.1306073269
## 715   715      1  91.24145 15.28978 9.369576 0.0745322369  2.2533183523
## 716   716      1 127.68318 14.30989 6.871591 0.2402927922  2.6850338857
## 717   717      1 112.68098 10.89020 2.901394 0.0784283669 -1.9111954758
## 718   718      1 101.08457 15.30609 5.962340 0.3888930355 -0.8916601043
## 719   719      1 115.31076 15.33232 6.467308 0.1211602176 -1.0759012942
## 720   720      1 126.28719 11.70984 9.588379 0.5414245313  0.6607392455
## 721   721      1 123.81912 12.80468 7.511002 0.3488636706  0.0745062826
## 722   722      1  77.39054 15.05622 4.947266 0.7906360670  0.7120185584
## 723   723      1 116.84576 12.78222 7.311625 0.8467163986  1.1011484964
## 724   724      1  81.20085 15.02889 3.618348 0.9407222481 -0.9136612054
## 725   725      1  92.42338 15.06198 2.745446 0.0849938842 -0.4395818437
## 726   726      1  81.92156 13.94442 1.638076 0.0634890683  2.7222137692
## 727   727      1  90.56563 12.57577 5.898903 0.0284334728 -2.2545883812
## 728   728      1  70.76862 10.35851 5.706363 0.4452790804 -2.2664028216
## 729   729      1 115.31251 15.14741 3.406150 0.6360279582 -0.8732262294
## 730   730      1 120.59893 10.09933 5.139453 0.4367471812 -1.8067311378
## 731   731      1  70.45134 14.38207 1.832447 0.8313998200  1.2516768788
## 732   732      1 110.65553 12.67180 9.078351 0.3344134788 -2.2028186797
## 733   733      1 121.51828 11.43801 9.361825 0.8673747515 -0.0767220656
## 734   734      1 117.18381 11.16589 3.787514 0.0885740428  0.5748809206
## 735   735      1  80.60761 13.15036 4.502737 0.5477184905 -0.6441491497
## 736   736      1  71.50789 11.85746 1.420443 0.8396393417  2.3202609062
## 737   737      1 125.91954 12.83866 2.205540 0.5141616028 -0.7529075569
## 738   738      1  74.18923 11.56498 7.107955 0.2379039100  1.2152466466
## 739   739      1 113.79396 12.91568 5.012497 0.9023067565 -0.3791664615
## 740   740      1 117.88156 13.92753 5.358877 0.2162190655  0.6195332093
## 741   741      1  80.42343 13.72521 2.931174 0.2822762718 -0.1222810949
## 742   742      1  65.88584 14.96211 2.559213 0.9062963116  0.3095557226
## 743   743      1 109.26618 12.68112 3.624593 0.1142329862 -2.1834231169
## 744   744      1 126.47545 13.26018 2.740696 0.9131322429 -2.2737748822
## 745   745      1  91.19318 12.92716 6.772593 0.0780302463 -1.3953665737
## 746   746      1 126.39357 14.92083 3.329297 0.6302305562  2.9016909843
## 747   747      1 127.62313 12.51275 2.532563 0.9769565023  1.6557653948
## 748   748      1 106.76317 10.56556 7.335490 0.6698698299  1.6104098930
## 749   749      1 125.09534 14.77543 4.240642 0.7636017499  2.8132133085
## 750   750      1  87.83891 13.68554 9.495127 0.3119425455 -1.0601716316
## 751   751      1  60.27105 12.39097 7.686155 0.2333122594  0.8097925471
## 752   752      1  99.85678 10.22363 4.098246 0.3478666586 -0.5563097386
## 753   753      1  64.74139 15.01595 6.550680 0.6191551220  2.0596254079
## 754   754      1  67.37266 10.78387 7.265543 0.5076509153  1.1454328389
## 755   755      1  92.95084 10.08584 1.410210 0.2035401447  3.1856837047
## 756   756      1  75.39162 15.45032 7.163066 0.4041950197 -4.4208359703
## 757   757      1  96.01163 11.00417 5.906387 0.6045738717  1.2724709117
## 758   758      1  68.46913 12.72527 6.304188 0.4330587834 -0.4913755079
## 759   759      1  88.12140 14.87703 5.720698 0.8176870900  0.6287511182
## 760   760      1 112.96867 11.23562 2.377429 0.8236676033  1.0246333094
## 761   761      1 111.91951 13.27487 5.364757 0.1566935449  2.0719683604
## 762   762      1  92.19133 13.96229 9.670211 0.9774178448  1.7750924228
## 763   763      1 100.74303 14.20989 9.593393 0.0645644146  0.0813698437
## 764   764      1 114.32064 10.68773 8.273775 0.9849790223 -2.6888605693
## 765   765      1 125.06143 12.24429 1.632132 0.0604971559 -1.0859874682
## 766   766      1 103.70969 12.89142 5.125113 0.1017172730  0.4195786119
## 767   767      1  64.59106 13.91322 5.276980 0.3318891332 -3.6679920561
## 768   768      1  75.23825 10.81800 4.450981 0.3178508370 -0.2952296468
## 769   769      1 101.79324 14.80426 7.422849 0.2061930094  1.5389415258
## 770   770      1 127.20311 11.84489 8.164508 0.1625500340  2.2114417622
## 771   771      1  73.66398 15.58306 1.862108 0.0193893774 -2.5715873958
## 772   772      1  96.99224 12.99637 5.854310 0.9413217974 -0.5081173674
## 773   773      1 101.29451 11.50823 7.389711 0.3911684838 -3.7793186740
## 774   774      1  94.22564 15.77714 3.647901 0.9678436790  1.8769998972
## 775   775      1 107.81657 15.66376 4.591316 0.1666842627  2.2910489156
## 776   776      1  90.21312 10.03248 5.610960 0.6123270872  0.8745474941
## 777   777      1  83.69636 12.55900 6.747173 0.1726096771 -0.7542645514
## 778   778      1  83.23125 14.86456 6.413297 0.7625138371  2.0116701719
## 779   779      1  67.03180 11.38445 2.736147 0.6905585239 -2.1986112913
## 780   780      1 108.83379 10.78142 8.107913 0.2595457942 -1.4857003831
## 781   781      1  90.16483 15.60871 3.591699 0.2113246762 -0.8462211749
## 782   782      1 122.50342 10.43665 8.256013 0.3982881645 -0.4156856434
## 783   783      1  96.28344 11.61515 9.787375 0.3187180622 -2.4187319510
## 784   784      1 126.62151 10.20898 4.573368 0.0075759876  2.0844811559
## 785   785      1 124.34863 11.53864 1.331378 0.1035330025  3.1636251523
## 786   786      1 100.61046 14.97924 4.020214 0.9156274013  0.6787734778
## 787   787      1  68.77793 10.23553 1.905364 0.0246044686 -2.9389304033
## 788   788      1 108.37788 13.12932 4.834754 0.4731256606 -0.1822501750
## 789   789      1  79.14754 13.27917 5.598132 0.3460128228  1.6842626624
## 790   790      1 116.47985 12.48641 5.497747 0.5027486840 -2.5038198132
## 791   791      1 106.40346 12.81383 5.527549 0.9255413855  0.6074556252
## 792   792      1  86.20887 11.66404 7.046780 0.4103619480 -1.7785932165
## 793   793      1  75.98902 13.87569 7.936954 0.3428693130 -1.9277166155
## 794   794      1  89.96464 10.40215 5.492007 0.6547787974 -0.0012034403
## 795   795      1 105.88686 13.65570 4.884320 0.1415023287 -0.2135737161
## 796   796      1  61.70159 11.11899 6.733630 0.5713806637 -1.1992227526
## 797   797      1 123.01168 10.37212 2.354061 0.3096808170  2.0000457087
## 798   798      1 127.23841 12.02772 5.566346 0.9314062106 -0.1026715620
## 799   799      1  78.82574 10.68667 3.936392 0.5444165596  0.3077376357
## 800   800      1  74.56045 14.33181 3.161112 0.4347603484 -0.8755362581
## 801   801      1 103.04756 13.61288 7.238580 0.8669892396 -1.2230288790
## 802   802      1  90.23729 10.38456 5.504120 0.2024095280 -0.2652672491
## 803   803      1 103.09829 14.77487 6.279299 0.5898167060 -3.1083640991
## 804   804      1  60.65577 11.43607 9.749152 0.7252991649  0.4748140525
## 805   805      1 113.69684 11.26409 1.608408 0.1194482700  1.8804115423
## 806   806      1  61.37126 10.27167 2.950859 0.3174538191  3.7010034117
## 807   807      1 120.18826 14.75629 8.863163 0.4298888594  1.3786734296
## 808   808      1  67.25077 10.25433 8.759610 0.6241753534  1.8459798248
## 809   809      1  63.21590 10.17846 1.831199 0.7842971964 -3.9719621357
## 810   810      1  65.09407 10.39706 8.210039 0.6825516310  0.1210419373
## 811   811      1 114.59318 10.14178 3.883834 0.5315038546  4.0242210509
## 812   812      1  77.13524 15.87034 4.506286 0.6899188310  0.5397521830
## 813   813      1  99.36500 14.02010 5.500532 0.4517551535  0.4124024934
## 814   814      1 108.87158 10.87220 9.893421 0.4595525835  0.9907693500
## 815   815      1  80.42127 15.60530 4.682741 0.9407198040  0.5435824007
## 816   816      1 114.28437 10.13735 6.086894 0.0426531816 -0.1980367109
## 817   817      1  76.73024 13.85878 2.009422 0.9896889930  1.5841679721
## 818   818      1 121.21070 12.98531 8.783619 0.1055218072  2.3929867331
## 819   819      1  77.27374 11.00620 2.188616 0.3504635149 -0.5152033023
## 820   820      1 129.53908 13.62537 8.909686 0.0935812439  0.7519342930
## 821   821      1  96.08745 15.31468 6.538444 0.5327423175 -2.9976096982
## 822   822      1  70.18645 13.23568 8.604733 0.2126297709  4.1332282071
## 823   823      1  61.47107 15.30044 4.080464 0.6754926480  0.3377128803
## 824   824      1 105.63517 12.44862 1.618994 0.4047276599  0.3047882194
## 825   825      1  97.71137 13.64662 8.217352 0.4126807321  0.9059592039
## 826   826      1 115.98743 14.39911 3.749829 0.9684331408 -2.4236570331
## 827   827      1  83.87986 13.34409 6.035016 0.8067069575 -0.2994612873
## 828   828      1  93.22830 14.18047 6.515390 0.9142884610  4.1050377917
## 829   829      1  64.06907 10.34899 4.332669 0.4721457071 -1.6652304396
## 830   830      1  68.56895 15.72803 9.625133 0.0564645401 -5.1113885458
## 831   831      1  77.55588 14.42155 5.560088 0.5032336442  2.4975727192
## 832   832      1 108.93512 11.38385 1.356874 0.6352648062  1.4488203438
## 833   833      1 109.29548 12.37215 6.592784 0.6839837197 -0.0940903635
## 834   834      1  96.39777 15.57890 2.556138 0.9081668651 -4.4366393246
## 835   835      1  96.97179 11.32585 5.774142 0.4443721652 -0.3992019413
## 836   836      1 106.77901 14.42406 5.919855 0.3380089903 -0.3382573968
## 837   837      1  72.84836 14.62182 9.804443 0.6171011208 -2.1288114226
## 838   838      1 116.97003 11.58655 8.971104 0.0549857740 -4.6227126873
## 839   839      1  74.20985 10.21168 8.914843 0.1507632060 -1.3763962995
## 840   840      1  96.92385 13.32468 2.053596 0.7684549892 -0.2794063498
## 841   841      1  69.84830 12.46388 1.979853 0.7525645487 -0.3649881107
## 842   842      1 127.85779 11.90338 4.921515 0.8348243576 -2.0622866870
## 843   843      1 104.64889 10.26605 7.558790 0.2743188040  1.3894132496
## 844   844      1  81.66816 12.92866 9.663810 0.2920360020  0.6273714177
## 845   845      1 104.68647 13.87309 5.969815 0.2304270824 -0.5943148122
## 846   846      1  91.47189 13.22779 7.726067 0.0227801919  0.6133857999
## 847   847      1  65.53870 15.56224 2.720228 0.0150705371  0.5899821156
## 848   848      1 129.00069 11.00713 5.031286 0.3535467375  1.0000464119
## 849   849      1 103.70789 12.00660 6.194293 0.6394315553 -2.1441499182
## 850   850      1  90.60185 14.22740 6.850071 0.4172186912  0.8563020981
## 851   851      1 114.64248 15.55674 9.063164 0.0209517733  1.6288513318
## 852   852      1 105.25225 10.04498 6.808241 0.1414858256 -3.0315069773
## 853   853      1  73.90359 11.67162 8.869080 0.8067720123 -4.7153049260
## 854   854      1  79.38880 13.08088 2.719555 0.5712682677 -1.7543625622
## 855   855      1  96.60399 12.03886 8.029391 0.8302758995 -1.3400605331
## 856   856      1 111.33236 12.70335 8.527125 0.7756017228  2.9109991493
## 857   857      1 118.94764 11.35659 5.192489 0.6426293838 -1.3255957182
## 858   858      1 124.88408 12.90453 6.783822 0.8395085728  2.3082244573
## 859   859      1  87.05293 10.76100 5.687115 0.2121135490  1.5913805543
## 860   860      1 111.78319 14.29005 8.277761 0.3151510174  2.2167607526
## 861   861      1  92.68646 15.62644 4.242102 0.6502662452  2.4378404524
## 862   862      1  86.35151 11.90323 2.372962 0.0155342680 -0.2159303953
## 863   863      1 105.93922 12.47210 6.445525 0.5657894390 -3.3238926091
## 864   864      1 100.19617 13.37891 3.479403 0.8989611943  1.3530014003
## 865   865      1 122.76925 14.21679 4.410105 0.9856144793 -0.7317918926
## 866   866      1 106.31799 14.66117 8.696831 0.8993575317 -1.6911112426
## 867   867      1 127.19361 10.86034 5.495156 0.7015993781 -1.6244742357
## 868   868      1  86.19069 15.67866 4.774034 0.5579089997  1.2243236922
## 869   869      1  95.59941 14.24013 2.360709 0.1581420209  0.6700088439
## 870   870      1  74.51388 10.91308 7.708526 0.8259845907 -0.8431860356
## 871   871      1  64.43735 11.07598 4.166244 0.6841743798 -0.4208812539
## 872   872      1 107.98331 13.97003 5.984136 0.4291387927 -0.0549393447
## 873   873      1 118.27705 12.70050 5.385417 0.9632956251  2.2894868187
## 874   874      1 111.72915 14.77709 4.254063 0.1636654702  0.9892619831
## 875   875      1  74.12670 13.03378 9.711435 0.4315551273 -0.6509221979
## 876   876      1 108.27296 12.92587 9.432193 0.8689757821 -1.6932189072
## 877   877      1  70.92381 12.71766 5.495539 0.6847803425 -1.8978846319
## 878   878      1 123.51517 12.57391 1.659225 0.7898183372  0.1541436508
## 879   879      1 103.03165 10.28767 5.455962 0.3719889789 -2.6062134052
## 880   880      1  70.03016 13.89464 8.203285 0.9975404097 -3.1849963911
## 881   881      1 106.80789 12.89588 1.114615 0.9528138617  1.0135934114
## 882   882      1  64.73123 11.45578 6.616902 0.9237347397  3.2824919708
## 883   883      1 119.29346 14.49262 8.517682 0.4056376314  1.3051484412
## 884   884      1 108.69345 11.99251 7.256328 0.6392724365 -1.0655708101
## 885   885      1 123.35904 11.81098 4.735285 0.7956720612  0.6086694165
## 886   886      1  93.95671 11.97898 1.730128 0.9969724836 -1.2945421216
## 887   887      1 128.99368 15.18829 6.038215 0.4148474743 -1.8370869537
## 888   888      1  96.64733 10.15426 7.926085 0.4397394927 -1.1509806475
## 889   889      1 108.98181 13.99794 7.751809 0.1993018554  0.3329667333
## 890   890      1  94.71827 12.24099 5.599176 0.7997770982 -2.3511533536
## 891   891      1 120.70019 15.59468 8.019638 0.3968722234 -1.5730254820
## 892   892      1 106.36639 13.92319 6.523463 0.7781228938  1.6239023928
## 893   893      1 102.63239 12.79297 5.860014 0.5898978186  2.7203915041
## 894   894      1  72.63083 11.82394 2.869431 0.5063792102 -0.3038405296
## 895   895      1  88.43415 11.55829 2.615742 0.3561927096 -2.7497631909
## 896   896      1 101.82796 11.56131 9.833745 0.9238783447  0.6040778580
## 897   897      1  67.25759 12.27861 4.589680 0.0677326338 -0.1444883537
## 898   898      1 129.73182 13.55151 1.370922 0.4628555330 -0.1455461295
## 899   899      1 110.94521 10.55461 5.070351 0.5125620537  0.6568316433
## 900   900      1 107.72422 15.73940 2.886229 0.8220927296  0.2079047062
## 901   901      1 112.21568 13.95345 5.486004 0.2332717043  2.6990489919
## 902   902      1  96.83041 10.66543 3.214323 0.1656776094  1.3064243819
## 903   903      1 105.43787 14.55392 3.411749 0.7707665192  1.8471542910
## 904   904      1  71.90629 12.51874 9.949316 0.5504564345 -2.1430557406
## 905   905      1 108.31261 13.61917 3.815743 0.2780532511  2.2228056379
## 906   906      1 101.01957 15.45406 3.386632 0.4239236799  0.5605311797
## 907   907      1  60.19315 12.34444 2.353853 0.0493758747  1.0524375413
## 908   908      1 109.32569 11.74253 6.995425 0.6465675947  0.2411211085
## 909   909      1 122.24687 10.44747 7.452284 0.4239445932 -0.7850421919
## 910   910      1 110.90773 12.43620 3.044645 0.8123932581 -1.4875101610
## 911   911      1  98.98280 11.54426 7.683160 0.6342692652  0.7843334517
## 912   912      1 124.17878 12.92696 3.106524 0.6520189301 -1.8688794208
## 913   913      1 102.10790 11.25958 6.750556 0.0106751563 -0.4334017928
## 914   914      1 124.63678 10.90601 5.556459 0.7617144666 -1.1733490455
## 915   915      1  60.95895 14.81319 5.344424 0.3204094048 -0.5127666478
## 916   916      1  72.95584 13.01927 5.004287 0.6506150973 -1.9880331557
## 917   917      1  75.65147 10.82894 4.924244 0.7463110066  2.4806263710
## 918   918      1 112.92436 13.01274 6.680388 0.9921975811 -2.0062611353
## 919   919      1 123.72942 11.04655 9.247372 0.6650407785 -1.9498350423
## 920   920      1 121.86737 14.69692 1.327561 0.5598950004 -1.1583522884
## 921   921      1  95.82485 13.91634 4.836299 0.9590055747  1.1041679242
## 922   922      1  95.54569 15.52681 8.421412 0.0211880857  0.3398467668
## 923   923      1 126.94678 12.80013 6.282144 0.6029123126 -2.1581765502
## 924   924      1 122.75353 15.43095 6.090838 0.2631914383 -0.1555298772
## 925   925      1 117.53787 13.00611 9.721841 0.2507068235  0.4696031392
## 926   926      1  73.13532 11.73671 9.482929 0.4781717146  2.8548461496
## 927   927      1 119.07623 13.03274 3.215020 0.0714573015 -3.1742873327
## 928   928      1  89.38015 14.35385 8.128842 0.4046197988 -2.1712038703
## 929   929      1  89.80057 11.30643 1.747814 0.2674128397 -0.5248261313
## 930   930      1 102.84492 11.62128 4.270279 0.9258768272  3.0127100099
## 931   931      1  66.51858 14.49753 6.233716 0.6565893402 -2.3368490461
## 932   932      1  67.34877 14.90068 7.985992 0.8190235386 -3.2831816381
## 933   933      1 110.30445 10.74669 7.257351 0.9546628832 -0.2222008216
## 934   934      1  92.35198 13.81905 2.584770 0.7458657927 -0.9771096680
## 935   935      1  69.38605 14.89276 3.273833 0.6618956525 -0.0519652853
## 936   936      1  71.51008 10.20110 4.001558 0.8282731059  3.1810893440
## 937   937      1  84.64076 12.38066 4.413688 0.3682986819 -2.5218669874
## 938   938      1  91.98762 12.33534 4.694032 0.3902498137  0.4197280514
## 939   939      1  74.82872 11.44689 9.607515 0.0763875970 -0.1364098430
## 940   940      1  73.88750 11.93869 2.381694 0.4127557455 -1.3072442070
## 941   941      1  67.06045 12.12979 4.230165 0.8024664996 -2.1428456072
## 942   942      1 121.19039 12.28839 4.136287 0.2154391315 -1.7739147931
## 943   943      1 121.51981 14.64885 4.162589 0.9980353138 -0.8388920597
## 944   944      1 109.12508 11.26791 1.366690 0.4498045584  4.0249342631
## 945   945      1 102.47449 10.48794 5.720330 0.4422812464  0.8174487967
## 946   946      1 123.68943 14.85840 3.176927 0.0434377382  4.2689973814
## 947   947      1  96.51747 12.88361 2.743403 0.7265394859 -0.4778035238
## 948   948      1 116.98921 14.01699 1.005104 0.6513465634 -3.2342598931
## 949   949      1  74.30882 10.59169 8.049193 0.9129053173  1.2054256124
## 950   950      1  96.46387 14.50453 4.958689 0.3402656501 -2.8514918618
## 951   951      1  85.33481 14.55324 5.625418 0.9730518488 -2.1673835389
## 952   952      1  69.45870 13.15271 7.473152 0.0634970439  1.9066691420
## 953   953      1  67.06190 11.33790 1.009375 0.4816362192 -2.5677827635
## 954   954      1  80.96301 14.06491 5.812191 0.1910568762  1.7819644684
## 955   955      1  71.24477 14.81386 9.220477 0.9967272545 -1.0080177245
## 956   956      1  64.17507 10.65176 2.718660 0.1790875897 -0.8697094361
## 957   957      1 126.50618 11.26048 4.440940 0.7913353522 -0.4806180259
## 958   958      1 112.87603 10.71037 7.065820 0.2989096609 -1.7246511037
## 959   959      1  71.08046 11.24802 5.941208 0.2845480100 -0.0319534007
## 960   960      1 102.52673 12.01703 6.606123 0.0421712250 -5.5356256417
## 961   961      1 102.51417 10.10904 9.863845 0.7293606452  0.4464276409
## 962   962      1 119.39540 11.36439 4.785019 0.9721764128  0.0177559392
## 963   963      1  92.52473 13.89096 1.952146 0.7568617254 -1.3909757964
## 964   964      1 103.65286 13.34701 8.842640 0.3359481078  3.2903410948
## 965   965      1  97.99204 13.69119 8.850792 0.9964917498  0.2630992463
## 966   966      1  77.02587 15.74889 5.321142 0.8294452664 -2.7128709776
## 967   967      1  78.38257 10.75087 4.742583 0.9529253186 -3.2980871293
## 968   968      1 122.66292 15.73787 7.974426 0.1396756303 -0.1757628238
## 969   969      1 127.42031 12.89283 7.313428 0.5842473472  2.9990931974
## 970   970      1  75.07706 12.66910 7.169634 0.2242697459 -2.8885069013
## 971   971      1  87.78635 15.76022 5.929715 0.6931879267 -2.7909455763
## 972   972      1 122.19044 12.41388 2.491964 0.6558009095  3.4980865438
## 973   973      1 109.90379 13.53608 3.059641 0.0738397685 -4.4044064732
## 974   974      1  81.45692 12.37662 5.439390 0.3746809852 -0.9408532934
## 975   975      1 110.39187 14.84879 4.851423 0.9011173144 -3.1615097369
## 976   976      1 110.38594 12.73479 8.136902 0.2016765780 -1.6325972682
## 977   977      1  76.84486 12.36896 7.032631 0.5741789762  1.1241698505
## 978   978      1  77.31594 15.14398 7.579990 0.3313007588 -0.8543313754
## 979   979      1  74.22767 13.58545 2.147123 0.3010862097  3.0128046921
## 980   980      1  77.01145 10.11523 9.417747 0.2384989471 -1.9421217497
## 981   981      1  93.64225 10.44021 3.879255 0.6555605242  2.3544427885
## 982   982      1 120.91979 13.14897 3.176853 0.6207212261  0.2648822435
## 983   983      1  77.89268 13.02247 2.231900 0.1668624172 -1.6969894734
## 984   984      1  94.91745 11.04675 8.563649 0.3212920043 -0.9738471310
## 985   985      1 103.10992 11.85934 2.452476 0.7801170920 -1.1302943187
## 986   986      1 117.36385 15.97449 3.825748 0.7465923594  1.8569017709
## 987   987      1 119.73978 13.78413 1.002572 0.2402267612 -3.5074006066
## 988   988      1  85.93774 13.14335 3.759584 0.3072390859 -1.9176750086
## 989   989      1 103.24354 13.82810 7.764957 0.0414880360 -1.0774093729
## 990   990      1  60.72923 10.74540 7.561107 0.5253195420  3.3730351171
## 991   991      1  94.90496 12.93416 6.781721 0.9968742153  3.5061253797
## 992   992      1  82.13074 11.33939 9.275298 0.7938808908  1.9667898968
## 993   993      1 114.29683 10.90511 3.657062 0.8973897772 -0.3510245384
## 994   994      1  84.45683 13.18158 1.687644 0.1906968970  1.0267294824
## 995   995      1  63.70844 14.60221 3.799787 0.8020162454  5.3355377772
## 996   996      1  82.37184 10.31899 5.716730 0.4440468918 -2.2989068764
## 997   997      1 125.33845 15.54976 4.131872 0.5687901990  0.8186723602
## 998   998      1  66.64182 11.25565 8.198279 0.6582111607  1.4435924914
## 999   999      1 111.40925 12.41786 5.430706 0.0177538309  1.5004109088
## 1000 1000      1 109.81406 13.50030 6.209681 0.6986729356  0.0697279733
##      size_centered natural_mortality fishing_mortality total_mortality
## 1     -28.15202814          63.15937         12.815203        75.97458
## 2       9.73802694          34.32599          9.026197        43.35219
## 3     -14.80981793          46.14795         11.480982        57.62894
## 4     -44.00198895          52.55088         14.400199        66.95108
## 5     -53.06790654          58.18634         15.306791        73.49313
## 6       7.99593676          35.32289          9.200406        44.52329
## 7       5.78847281          49.06234          9.421153        58.48349
## 8       1.26553241          50.52898          9.873447        60.40242
## 9     -55.65018068          60.29019         15.565018        75.85521
## 10    -47.19913332          66.14002         14.719913        80.85993
## 11    -27.39518695          57.61867         12.739519        70.35819
## 12     -7.11851308          51.94405         10.711851        62.65590
## 13     -9.82301458          44.34322         10.982301        55.32552
## 14    -37.40956812          51.01106         13.740957        64.75202
## 15    -18.73796023          59.21142         11.873796        71.08522
## 16    -59.50006015          71.67317         15.950006        87.62318
## 17    -27.88542670          61.70522         12.788543        74.49376
## 18      5.95653962          45.43845          9.404346        54.84280
## 19    -29.97966936          49.22209         12.997967        62.22005
## 20    -44.53197982          61.37767         14.453198        75.83087
## 21      3.57829048          44.56468          9.642171        54.20685
## 22      3.77113494          33.03910          9.622887        42.66198
## 23      0.39111078          47.67347          9.960889        57.63436
## 24    -21.48898532          57.11025         12.148899        69.25915
## 25    -45.48701716          52.35702         14.548702        66.90572
## 26      7.88723896          41.97479          9.211276        51.18607
## 27     -4.44116585          49.39305         10.444117        59.83717
## 28     -2.58032347          55.75123         10.258032        66.00926
## 29    -38.46509352          55.20394         13.846509        69.05045
## 30    -29.47059447          52.94153         12.947059        65.88859
## 31    -50.54346428          69.46457         15.054346        84.51891
## 32      2.93853257          44.99207          9.706147        54.69821
## 33     -7.57775693          47.92161         10.757776        58.67938
## 34    -14.64168056          44.86001         11.464168        56.32418
## 35     -3.85188379          44.68486         10.385188        55.07005
## 36    -32.80705266          55.86843         13.280705        69.14913
## 37     -7.03004105          53.40726         10.703004        64.11026
## 38    -22.73925059          49.18913         12.273925        61.46306
## 39    -54.78259602          58.01931         15.478260        73.49757
## 40     -0.18577813          44.72147         10.018578        54.74005
## 41    -37.39579936          53.29409         13.739580        67.03367
## 42    -47.71972981          72.45630         14.771973        87.22827
## 43    -53.60599381          62.99508         15.360599        78.35568
## 44    -43.29531692          55.82246         14.329532        70.15199
## 45    -54.39387111          63.11630         15.439387        78.55569
## 46    -23.95810687          60.64516         12.395811        73.04097
## 47    -40.96142628          49.43411         14.096143        63.53026
## 48    -57.43572895          71.39443         15.743573        87.13801
## 49    -30.42546002          45.84000         13.042546        58.88255
## 50    -54.48653892          67.56412         15.448654        83.01278
## 51    -21.61749583          57.03832         12.161750        69.20007
## 52     -4.88587265          46.93592         10.488587        57.42451
## 53    -47.15175600          67.76128         14.715176        82.47645
## 54     -5.79978781          37.90422         10.579979        48.48420
## 55    -55.49004926          59.38890         15.549005        74.93790
## 56    -51.78427556          65.07160         15.178428        80.25002
## 57      3.01383919          43.49719          9.698616        53.19581
## 58      9.01977136          32.23600          9.098023        41.33402
## 59    -41.22194966          66.44825         14.122195        80.57045
## 60    -34.75317537          59.81267         13.475318        73.28798
## 61      0.20414375          45.30780          9.979586        55.28738
## 62      0.31826792          52.57231          9.968173        62.54048
## 63    -12.93477402          40.66326         11.293477        51.95674
## 64      2.91898229          47.81354          9.708102        57.52164
## 65    -31.32953272          52.39754         13.132953        65.53049
## 66     -0.02402870          35.66609         10.002403        45.66849
## 67    -43.53692958          62.00912         14.353693        76.36282
## 68    -24.16963140          50.40104         12.416963        62.81801
## 69    -11.46065338          44.48495         11.146065        55.63101
## 70    -24.49224963          55.69521         12.449225        68.14444
## 71    -43.98733754          65.86360         14.398734        80.26233
## 72    -53.57899859          53.81248         15.357900        69.17038
## 73    -26.64028460          61.78969         12.664028        74.45372
## 74    -19.43021676          65.74349         11.943022        77.68651
## 75     -4.72436075          49.15007         10.472436        59.62250
## 76    -20.20454316          56.81359         12.020454        68.83404
## 77    -41.78469197          59.86728         14.178469        74.04575
## 78    -24.49704107          62.41454         12.449704        74.86425
## 79    -47.39695419          61.20351         14.739695        75.94320
## 80    -13.60222616          38.47154         11.360223        49.83176
## 81    -21.28175770          57.01405         12.128176        69.14223
## 82    -43.31603968          59.13247         14.331604        73.46407
## 83      2.23963026          45.59372          9.776037        55.36975
## 84    -34.14484815          62.17610         13.414485        75.59058
## 85      9.76453328          38.11146          9.023547        47.13501
## 86    -55.90663416          68.57009         15.590663        84.16075
## 87    -36.62264726          55.41159         13.662265        69.07386
## 88    -12.39365911          55.16194         11.239366        66.40131
## 89    -59.16252666          68.13981         15.916253        84.05606
## 90    -45.50793759          60.03452         14.550794        74.58531
## 91      9.32136579          38.70153          9.067863        47.76939
## 92    -39.55127220          56.03171         13.955127        69.98683
## 93    -36.47455369          49.62326         13.647455        63.27072
## 94      8.79096380          48.02738          9.120904        57.14829
## 95    -23.61844745          57.00194         12.361845        69.36379
## 96    -43.00011044          67.08855         14.300011        81.38856
## 97    -14.93612675          43.19588         11.493613        54.68949
## 98    -44.68661625          72.03557         14.468662        86.50423
## 99     -2.60121093          41.68809         10.260121        51.94821
## 100   -20.10698515          61.54899         12.010699        73.55969
## 101   -31.33207443          46.45028         13.133207        59.58349
## 102   -55.31118121          65.41380         15.531118        80.94492
## 103   -40.12062259          69.81325         14.012062        83.82532
## 104   -44.58914897          56.56458         14.458915        71.02349
## 105   -54.42420427          61.21914         15.442420        76.66156
## 106   -22.60879108          61.36140         12.260879        73.62228
## 107   -29.51267834          63.11222         12.951268        76.06349
## 108   -33.73323188          51.63443         13.373323        65.00776
## 109   -56.65111234          73.14060         15.665111        88.80571
## 110    -8.34353915          58.48017         10.834354        69.31453
## 111   -41.20912498          59.98742         14.120912        74.10833
## 112   -59.93841814          74.68376         15.993842        90.67760
## 113   -11.66554000          48.75910         11.166554        59.92565
## 114   -35.89986802          46.22514         13.589987        59.81513
## 115   -12.69662333          48.40374         11.269662        59.67340
## 116   -29.18637647          58.21832         12.918638        71.13696
## 117     7.12403785          41.54641          9.287596        50.83400
## 118    -4.86343302          50.22172         10.486343        60.70807
## 119     3.22935841          41.71874          9.677064        51.39580
## 120   -59.59425142          64.42625         15.959425        80.38568
## 121   -37.68228019          57.05983         13.768228        70.82806
## 122   -12.58731102          55.31664         11.258731        66.57537
## 123     6.82869440          34.90126          9.317131        44.21839
## 124     0.77481151          45.36441          9.922519        55.28693
## 125   -31.36255421          54.24383         13.136255        67.38009
## 126   -58.97132924          58.66144         15.897133        74.55858
## 127   -19.65649931          44.85050         11.965650        56.81615
## 128   -32.15744648          56.81300         13.215745        70.02874
## 129     4.22558628          37.05369          9.577441        46.63114
## 130   -32.23023517          63.85078         13.223024        77.07381
## 131   -36.28070609          67.33413         13.628071        80.96220
## 132   -27.20014819          42.86177         12.720015        55.58179
## 133    -8.76055503          35.23736         10.876056        46.11342
## 134   -44.76933238          65.72411         14.476933        80.20104
## 135     6.52360004          44.56029          9.347640        53.90793
## 136   -41.71730737          69.34164         14.171731        83.51337
## 137   -57.78944673          57.88776         15.778945        73.66670
## 138   -15.89964513          43.49657         11.589965        55.08653
## 139   -52.77201054          71.40787         15.277201        86.68507
## 140   -27.59750016          43.38842         12.759750        56.14817
## 141   -39.19176306          63.80045         13.919176        77.71963
## 142   -55.43107678          64.27713         15.543108        79.82024
## 143   -12.64301677          54.60984         11.264302        65.87414
## 144   -31.92712251          55.12866         13.192712        68.32138
## 145   -33.01891655          54.81734         13.301892        68.11923
## 146     9.28548601          40.23451          9.071451        49.30596
## 147   -59.55827995          68.49818         15.955828        84.45400
## 148   -31.67747538          62.15352         13.167748        75.32127
## 149   -13.24989367          56.83064         11.324989        68.15563
## 150   -47.56645544          64.30023         14.756646        79.05688
## 151   -47.21242151          70.41130         14.721242        85.13254
## 152    -6.76043184          54.50287         10.676043        65.17891
## 153   -43.06804784          62.88993         14.306805        77.19674
## 154     5.14670834          36.73272          9.485329        46.21805
## 155     4.31938543          46.75000          9.568061        56.31806
## 156   -54.21455657          61.97504         15.421456        77.39650
## 157   -14.60880590          52.26467         11.460881        63.72555
## 158   -41.71951521          69.70082         14.171952        83.87277
## 159   -21.79087868          50.36988         12.179088        62.54897
## 160   -32.90969851          56.00217         13.290970        69.29314
## 161   -17.20024317          47.73043         11.720024        59.45046
## 162   -34.17880879          56.68408         13.417881        70.10196
## 163    -5.46857205          50.83254         10.546857        61.37940
## 164   -59.30827988          69.24897         15.930828        85.17980
## 165   -32.92551780          63.92415         13.292552        77.21670
## 166     6.37841911          53.31790          9.362158        62.68006
## 167   -37.71370603          59.40793         13.771371        73.17930
## 168   -45.48552862          58.75989         14.548553        73.30844
## 169   -25.08077784          48.48923         12.508078        60.99731
## 170   -18.57599769          59.41094         11.857600        71.26854
## 171   -43.60126090          56.89836         14.360126        71.25849
## 172   -15.32177647          53.64727         11.532178        65.17944
## 173    -8.98685715          49.72170         10.898686        60.62039
## 174    -5.90454477          51.26849         10.590454        61.85895
## 175   -11.82091762          48.98129         11.182092        60.16338
## 176   -43.87712404          58.99988         14.387712        73.38759
## 177   -24.37298220          55.67226         12.437298        68.10956
## 178   -42.66836758          51.87319         14.266837        66.14003
## 179   -58.25629032          73.44492         15.825629        89.27055
## 180    -1.18927109          39.58136         10.118927        49.70029
## 181   -45.21598673          68.31483         14.521599        82.83642
## 182    -7.03706222          48.83176         10.703706        59.53547
## 183    -6.53129105          45.16240         10.653129        55.81553
## 184   -37.73464354          62.94566         13.773464        76.71912
## 185   -16.80767700          60.27289         11.680768        71.95366
## 186     5.64553464          46.88441          9.435447        56.31985
## 187   -45.32101245          61.95208         14.532101        76.48418
## 188    -5.92341356          45.71238         10.592341        56.30473
## 189   -32.17893511          54.30301         13.217894        67.52090
## 190   -48.73614143          68.57484         14.873614        83.44845
## 191     1.94683065          41.53411          9.805317        51.33942
## 192   -15.31951525          38.73594         11.531952        50.26790
## 193    -7.58430392          48.32015         10.758430        59.07858
## 194     9.11124597          25.06228          9.088875        34.15116
## 195    -1.64302519          54.04527         10.164303        64.20957
## 196   -27.13041464          49.76046         12.713041        62.47350
## 197   -51.90527450          55.85741         15.190527        71.04794
## 198   -22.66812008          63.04635         12.266812        75.31316
## 199   -33.02267992          60.49694         13.302268        73.79921
## 200    -1.81201306          42.26369         10.181201        52.44489
## 201   -59.10314685          60.13295         15.910315        76.04326
## 202   -23.60609813          59.67025         12.360610        72.03085
## 203   -36.95962268          53.72159         13.695962        67.41755
## 204   -33.88772937          67.60982         13.388773        80.99859
## 205   -34.41350969          50.36535         13.441351        63.80670
## 206   -44.04290082          64.60189         14.404290        79.00618
## 207    -8.09209591          56.16776         10.809210        66.97697
## 208    -6.35932414          46.23121         10.635932        56.86714
## 209   -44.44137452          57.10823         14.444137        71.55237
## 210    -3.89402793          47.14033         10.389403        57.52973
## 211    -3.64800721          39.39551         10.364801        49.76031
## 212   -17.74043798          47.98719         11.774044        59.76124
## 213   -44.27400504          62.57074         14.427401        76.99814
## 214    -7.65562134          58.50079         10.765562        69.26636
## 215   -30.17592035          50.61069         13.017592        63.62828
## 216    -1.43590003          46.10327         10.143590        56.24686
## 217    -5.49223091          47.74640         10.549223        58.29562
## 218     8.01820702          30.62032          9.198179        39.81850
## 219     5.92705271          49.52418          9.407295        58.93148
## 220   -56.94888618          66.12955         15.694889        81.82444
## 221   -41.02503433          56.73607         14.102503        70.83858
## 222   -40.37130262          57.13442         14.037130        71.17155
## 223     5.05344884          35.94580          9.494655        45.44046
## 224   -14.78871153          52.88525         11.478871        64.36412
## 225   -47.98961684          65.56372         14.798962        80.36268
## 226     9.29865772          50.66008          9.070134        59.73021
## 227   -43.69982315          69.61211         14.369982        83.98209
## 228     2.25918813          43.42085          9.774081        53.19493
## 229   -59.69715224          60.55524         15.969715        76.52496
## 230   -23.47934040          54.84414         12.347934        67.19207
## 231   -21.42956720          58.25496         12.142957        70.39792
## 232   -27.90995715          54.95169         12.790996        67.74269
## 233   -40.58526660          68.62088         14.058527        82.67940
## 234   -26.40487957          47.85462         12.640488        60.49510
## 235    -9.97190229          54.98091         10.997190        65.97810
## 236    -7.23198709          41.04920         10.723199        51.77240
## 237    -7.60353706          48.12156         10.760354        58.88191
## 238   -49.40105193          67.80565         14.940105        82.74575
## 239     1.61797615          32.79985          9.838202        42.63805
## 240   -41.87686950          57.75583         14.187687        71.94351
## 241   -44.58048553          63.96637         14.458049        78.42442
## 242   -36.89031308          61.33567         13.689031        75.02470
## 243   -41.11248391          57.37477         14.111248        71.48601
## 244   -34.88717559          62.21540         13.488718        75.70412
## 245   -27.11219597          58.21186         12.711220        70.92307
## 246   -16.82550550          51.95532         11.682551        63.63787
## 247   -46.97591137          60.15834         14.697591        74.85593
## 248    -4.67146801          39.41889         10.467147        49.88603
## 249     5.86510585          33.07533          9.413489        42.48882
## 250    -3.82963278          49.55852         10.382963        59.94148
## 251   -57.07384148          70.51813         15.707384        86.22551
## 252   -31.36967233          55.59825         13.136967        68.73522
## 253   -36.78141774          72.81373         13.678142        86.49187
## 254   -16.92469721          49.63975         11.692470        61.33222
## 255   -57.26940790          60.08991         15.726941        75.81685
## 256    -7.18701815          45.92610         10.718702        56.64480
## 257   -57.61930691          62.70264         15.761931        78.46457
## 258    -2.16622928          35.72982         10.216623        45.94644
## 259   -39.44901278          55.82990         13.944901        69.77480
## 260   -37.42457097          63.15946         13.742457        76.90191
## 261    -8.75459853          38.61122         10.875460        49.48668
## 262   -46.22109609          74.44511         14.622110        89.06722
## 263    -7.96522595          42.83978         10.796523        53.63630
## 264   -24.15315989          45.58378         12.415316        57.99910
## 265   -48.94948754          59.85101         14.894949        74.74596
## 266    -0.35781910          41.38227         10.035782        51.41805
## 267   -41.33255559          61.94188         14.133256        76.07513
## 268   -41.01503017          65.02971         14.101503        79.13121
## 269   -27.25018948          51.27579         12.725019        64.00081
## 270   -36.11071147          64.33842         13.611071        77.94949
## 271   -36.36459465          68.71752         13.636459        82.35398
## 272   -53.16793276          71.15038         15.316793        86.46718
## 273   -53.04286565          62.27858         15.304287        77.58287
## 274     4.62655124          44.60763          9.537345        54.14497
## 275   -39.63320094          58.44764         13.963320        72.41096
## 276   -53.70606475          77.28360         15.370606        92.65420
## 277   -21.83496404          54.39954         12.183496        66.58303
## 278     6.19212414          38.28313          9.380788        47.66392
## 279    -5.35649062          48.48101         10.535649        59.01666
## 280     5.53642848          45.00698          9.446357        54.45333
## 281    -9.54831281          45.20133         10.954831        56.15616
## 282   -50.77109302          60.65759         15.077109        75.73470
## 283   -33.96787862          52.78200         13.396788        66.17878
## 284   -48.69809633          73.56208         14.869810        88.43189
## 285   -27.47702616          58.15855         12.747703        70.90626
## 286     9.20653737          48.73614          9.079346        57.81549
## 287   -46.14110457          67.89080         14.614110        82.50491
## 288   -14.75412290          44.73862         11.475412        56.21403
## 289    -9.43474524          39.41346         10.943475        50.35693
## 290   -20.18497818          44.98791         12.018498        57.00641
## 291   -40.55467914          63.45304         14.055468        77.50850
## 292   -22.88168900          49.82474         12.288169        62.11291
## 293   -51.94548854          69.45743         15.194549        84.65198
## 294    -2.83819587          45.90797         10.283820        56.19179
## 295   -57.28588677          62.66419         15.728589        78.39278
## 296   -25.98100328          57.00060         12.598100        69.59870
## 297   -34.68369055          54.71410         13.468369        68.18247
## 298   -14.61251368          52.64026         11.461251        64.10151
## 299   -52.90465115          70.66816         15.290465        85.95862
## 300   -56.62047421          70.56500         15.662047        86.22705
## 301    -7.04367296          46.42662         10.704367        57.13098
## 302   -25.36662291          54.10082         12.536662        66.63748
## 303    -0.25156034          46.54984         10.025156        56.57499
## 304   -51.58538150          57.90885         15.158538        73.06738
## 305    -5.62166165          57.06623         10.562166        67.62840
## 306    -8.45875796          38.22783         10.845876        49.07371
## 307   -58.66566247          65.70126         15.866566        81.56783
## 308   -30.62558519          53.00701         13.062559        66.06957
## 309   -18.29533772          52.95884         11.829534        64.78837
## 310   -35.49791373          62.82008         13.549791        76.36987
## 311    -5.22842230          51.88940         10.522842        62.41224
## 312     7.64463455          36.34576          9.235537        45.58130
## 313   -23.73692952          55.28238         12.373693        67.65607
## 314   -46.17602377          59.45994         14.617602        74.07755
## 315     4.18535629          34.98048          9.581464        44.56195
## 316   -27.37216426          55.89900         12.737216        68.63621
## 317   -47.66738604          64.41607         14.766739        79.18281
## 318   -41.33395863          53.33062         14.133396        67.46401
## 319   -14.89706374          50.45556         11.489706        61.94527
## 320   -18.90649736          49.13616         11.890650        61.02681
## 321   -31.76970604          65.91234         13.176971        79.08931
## 322   -39.59471825          63.21211         13.959472        77.17158
## 323    -0.51804729          41.18762         10.051805        51.23943
## 324    -9.94356195          46.62683         10.994356        57.62119
## 325    -1.16891565          40.11418         10.116892        50.23107
## 326     2.08454750          35.35607          9.791545        45.14761
## 327     0.41552876          55.60824          9.958447        65.56668
## 328   -20.43066778          54.01519         12.043067        66.05826
## 329   -58.08967871          64.21716         15.808968        80.02613
## 330   -18.60798963          51.94761         11.860799        63.80841
## 331    -6.46320877          55.44625         10.646321        66.09257
## 332     7.05012001          44.90299          9.294988        54.19798
## 333   -12.42000911          45.34039         11.242001        56.58239
## 334   -29.36726092          60.76214         12.936726        73.69886
## 335   -58.12745882          61.01574         15.812746        76.82849
## 336    -0.43187368          51.26850         10.043187        61.31169
## 337   -34.71012214          48.68936         13.471012        62.16037
## 338     4.69933725          48.46924          9.530066        57.99930
## 339     5.11815445          47.39565          9.488185        56.88384
## 340   -52.04344473          73.63475         15.204344        88.83910
## 341    -4.99880763          49.75439         10.499881        60.25427
## 342   -44.64451139          68.70717         14.464451        83.17162
## 343   -48.79930497          62.57560         14.879930        77.45553
## 344   -27.99829590          52.62721         12.799830        65.42704
## 345   -57.09986848          65.76416         15.709987        81.47415
## 346   -35.21415776          58.10669         13.521416        71.62810
## 347   -35.98532190          68.90689         13.598532        82.50543
## 348   -28.01838121          46.38761         12.801838        59.18945
## 349   -20.84369963          45.01283         12.084370        57.09720
## 350   -40.98848296          65.63908         14.098848        79.73792
## 351   -19.82501844          60.55865         11.982502        72.54116
## 352     5.50333726          41.64973          9.449666        51.09940
## 353   -58.70804084          57.25646         15.870804        73.12726
## 354     1.13756622          43.06972          9.886243        52.95597
## 355    -2.37423806          45.00830         10.237424        55.24572
## 356   -51.66215002          61.37475         15.166215        76.54096
## 357   -47.18918335          72.91858         14.718918        87.63750
## 358    -8.24999678          43.83584         10.825000        54.66084
## 359   -42.73240355          65.98460         14.273240        80.25784
## 360     6.43385913          33.01199          9.356614        42.36860
## 361   -33.67608902          62.14928         13.367609        75.51688
## 362    -1.35426298          43.19722         10.135426        53.33264
## 363   -48.99633600          63.19070         14.899634        78.09033
## 364   -30.32003976          52.44538         13.032004        65.47738
## 365    -9.21450232          48.44317         10.921450        59.36462
## 366   -55.85365844          69.03377         15.585366        84.61913
## 367   -18.84452728          55.91385         11.884453        67.79831
## 368   -18.79467473          57.04632         11.879467        68.92578
## 369   -24.47585074          53.45292         12.447585        65.90050
## 370    -7.71905784          52.93004         10.771906        63.70194
## 371     2.37168303          45.28910          9.762832        55.05193
## 372   -52.62364078          58.08535         15.262364        73.34771
## 373     5.03400734          34.96716          9.496599        44.46376
## 374   -52.36958388          58.33037         15.236958        73.56732
## 375   -33.08364514          59.48274         13.308365        72.79111
## 376   -41.36186487          54.74705         14.136186        68.88324
## 377   -49.59209158          66.08503         14.959209        81.04424
## 378     6.64363314          50.23211          9.335637        59.56775
## 379    -8.50249929          49.32827         10.850250        60.17852
## 380    -1.07375186          42.49442         10.107375        52.60179
## 381    -3.73469051          40.19715         10.373469        50.57062
## 382    -1.80765673          41.19467         10.180766        51.37544
## 383   -59.41577477          70.11324         15.941577        86.05481
## 384     9.23948080          42.57953          9.076052        51.65558
## 385   -56.61279038          74.75312         15.661279        90.41440
## 386   -43.38003938          58.56277         14.338004        72.90078
## 387   -30.35098237          56.11236         13.035098        69.14746
## 388     6.14996663          42.45661          9.385003        51.84162
## 389    -8.16497698          41.61073         10.816498        52.42723
## 390   -15.85627065          48.00672         11.585627        59.59234
## 391     7.57914767          31.56665          9.242085        40.80874
## 392   -40.63614416          60.53619         14.063614        74.59981
## 393   -10.12664819          52.02436         11.012665        63.03702
## 394   -51.92978548          66.06520         15.192979        81.25817
## 395   -36.82194564          56.60127         13.682195        70.28347
## 396   -25.29246563          51.80712         12.529247        64.33637
## 397   -30.74527691          57.18548         13.074528        70.26001
## 398   -41.32723865          66.15976         14.132724        80.29249
## 399   -17.00905928          54.79331         11.700906        66.49422
## 400    -4.14362007          46.32948         10.414362        56.74384
## 401    -7.37662795          44.34001         10.737663        55.07767
## 402     5.05604105          42.94510          9.494396        52.43949
## 403   -35.46697599          57.40781         13.546698        70.95451
## 404   -40.75632621          57.85338         14.075633        71.92901
## 405     4.63395305          47.07336          9.536605        56.60996
## 406   -39.66281658          59.82247         13.966282        73.78875
## 407   -49.18654036          66.02430         14.918654        80.94295
## 408   -41.23197661          62.84742         14.123198        76.97061
## 409   -56.18240005          57.82243         15.618240        73.44067
## 410     6.30011858          42.21764          9.369988        51.58763
## 411   -29.38283057          47.95627         12.938283        60.89455
## 412   -53.09985749          55.77414         15.309986        71.08412
## 413   -52.78102286          72.61308         15.278102        87.89118
## 414     4.39063000          38.57625          9.560937        48.13718
## 415     1.80266283          45.86650          9.819734        55.68624
## 416   -27.06599316          60.86880         12.706599        73.57540
## 417     8.41527425          44.23551          9.158473        53.39398
## 418   -13.36803195          53.54379         11.336803        64.88059
## 419   -27.99370434          54.09304         12.799370        66.89241
## 420    -4.54364770          47.07653         10.454365        57.53089
## 421     4.93580399          46.35599          9.506420        55.86241
## 422   -50.19398646          66.96128         15.019399        81.98068
## 423   -15.14282442          44.87562         11.514282        56.38990
## 424   -25.90609977          60.60099         12.590610        73.19160
## 425    -9.87785057          56.17188         10.987785        67.15967
## 426   -17.37835130          64.06657         11.737835        75.80440
## 427    -4.54183548          48.98970         10.454184        59.44388
## 428     4.62324400          45.66304          9.537676        55.20071
## 429    -5.94852137          58.60285         10.594852        69.19770
## 430    -9.85168142          44.56989         10.985168        55.55505
## 431   -28.93240144          54.82912         12.893240        67.72236
## 432   -48.82476067          65.89403         14.882476        80.77651
## 433   -50.60943089          71.26566         15.060943        86.32660
## 434    -3.59830067          45.42443         10.359830        55.78426
## 435   -34.44942310          56.39353         13.444942        69.83847
## 436     4.45650151          43.17347          9.554350        52.72782
## 437     5.07443350          37.94485          9.492557        47.43741
## 438   -14.22826610          48.89596         11.422827        60.31879
## 439   -24.66439950          51.76305         12.466440        64.22949
## 440   -13.82836460          48.78387         11.382836        60.16670
## 441   -26.24007085          57.96927         12.624007        70.59328
## 442   -20.31364126          44.97999         12.031364        57.01136
## 443    -9.05285237          51.37589         10.905285        62.28117
## 444     6.87973041          39.30401          9.312027        48.61604
## 445   -48.19782282          61.30667         14.819782        76.12646
## 446   -23.12035664          44.05348         12.312036        56.36552
## 447   -39.79683210          62.52171         13.979683        76.50139
## 448   -10.20390607          43.82986         11.020391        54.85025
## 449    -1.09209936          50.62372         10.109210        60.73293
## 450     3.31740951          41.07352          9.668259        50.74178
## 451   -37.97666251          58.20459         13.797666        72.00226
## 452   -12.74575956          50.06712         11.274576        61.34169
## 453   -19.43703492          52.34679         11.943703        64.29050
## 454   -17.68123201          55.18811         11.768123        66.95623
## 455   -37.28018303          61.73974         13.728018        75.46776
## 456   -20.82040402          48.62354         12.082040        60.70558
## 457   -45.28860299          64.59594         14.528860        79.12481
## 458   -59.09151916          57.62247         15.909152        73.53162
## 459   -42.16179186          62.50858         14.216179        76.72476
## 460   -25.59529382          50.24906         12.559529        62.80859
## 461    -4.52792751          45.76251         10.452793        56.21531
## 462     5.86325261          28.19634          9.413675        37.61002
## 463   -53.16864021          72.65967         15.316864        87.97653
## 464   -18.60427025          48.56739         11.860427        60.42782
## 465   -41.73648478          64.58366         14.173648        78.75731
## 466     3.01473490          48.24205          9.698527        57.94058
## 467     8.93526357          48.62149          9.106474        57.72796
## 468   -52.31920496          63.63094         15.231920        78.86286
## 469     6.55173640          36.38432          9.344826        45.72914
## 470   -15.22121416          48.78225         11.522121        60.30437
## 471    -7.53228855          47.20942         10.753229        57.96265
## 472   -49.98156594          69.92223         14.998157        84.92038
## 473   -15.03285759          55.86067         11.503286        67.36396
## 474     0.07682430          46.33908          9.992318        56.33139
## 475   -26.48082024          46.37273         12.648082        59.02081
## 476   -44.37721181          64.61921         14.437721        79.05694
## 477   -53.71092616          62.56910         15.371093        77.94019
## 478   -25.74665564          40.44953         12.574666        53.02419
## 479   -49.13539117          64.75589         14.913539        79.66943
## 480   -58.12177124          65.07585         15.812177        80.88803
## 481   -36.84841703          52.96968         13.684842        66.65453
## 482   -49.11990911          63.40885         14.911991        78.32084
## 483   -10.54196642          40.33816         11.054197        51.39236
## 484   -56.28804207          62.38610         15.628804        78.01490
## 485   -28.99761603          45.51454         12.899762        58.41430
## 486     0.79542422          45.66311          9.920458        55.58357
## 487   -56.23431504          73.97065         15.623432        89.59408
## 488   -42.90421758          64.54972         14.290422        78.84014
## 489   -49.32135183          58.68276         14.932135        73.61490
## 490   -11.53604622          53.30448         11.153605        64.45808
## 491   -10.30871680          57.69094         11.030872        68.72182
## 492   -42.42642768          61.46204         14.242643        75.70469
## 493   -18.11698658          49.08669         11.811699        60.89839
## 494   -53.32280671          70.11596         15.332281        85.44825
## 495   -24.86152716          63.80853         12.486153        76.29469
## 496   -29.77429099          49.07624         12.977429        62.05367
## 497     7.96815910          46.60783          9.203184        55.81101
## 498     3.55535802          44.07519          9.644464        53.71965
## 499    -7.53902301          43.43346         10.753902        54.18737
## 500   -16.75025618          54.31710         11.675026        65.99213
## 501     1.09374510          40.85429         30.437498        71.29179
## 502    56.32808571          31.42105         52.531234        83.95228
## 503    -9.29430179          54.31849         26.282279        80.60077
## 504    41.51296779          23.02907         46.605187        69.63425
## 505    29.72687739          33.10406         41.890751        74.99481
## 506    56.47105993          14.53378         52.588424        67.12220
## 507    37.62346478          30.90796         45.049386        75.95734
## 508    28.77176538          33.53932         41.508706        75.04803
## 509    -4.83484684          52.39162         28.066061        80.45768
## 510     7.10812525          43.26229         32.843250        76.10554
## 511    20.69457047          39.95148         38.277828        78.22931
## 512    11.12944584          32.94629         34.451778        67.39807
## 513    31.56571830          42.99371         42.626287        85.61999
## 514    28.35120635          28.43592         41.340483        69.77640
## 515    35.74415926          26.12144         44.297664        70.41911
## 516    56.65594068          33.91529         52.662376        86.57766
## 517    18.09558125          33.26651         37.238232        70.50474
## 518    20.82187025          39.38305         38.328748        77.71180
## 519    40.09623740          24.32017         46.038495        70.35866
## 520    52.90750357          22.72828         51.163001        73.89128
## 521    13.56281098          33.46457         35.425124        68.88969
## 522    35.39671102          27.17569         44.158684        71.33438
## 523    54.72976276          33.77115         51.891905        85.66306
## 524    51.64639175          23.65931         50.658557        74.31786
## 525     8.16460289          42.14421         33.265841        75.41005
## 526     7.50126881          46.84958         33.000508        79.85009
## 527    11.66920420          38.37705         34.667682        73.04473
## 528    29.07611912          29.84890         41.630448        71.47935
## 529    19.99200198          35.32323         37.996801        73.32003
## 530    17.86177179          41.04391         37.144709        78.18862
## 531    42.86844597          24.48427         47.147378        71.63165
## 532     8.92797728          36.86376         33.571191        70.43495
## 533    13.26195699          29.01084         35.304783        64.31562
## 534    49.68930909          18.11568         49.875724        67.99141
## 535    52.96620447          24.98849         51.186482        76.17497
## 536    43.31713728          36.88510         47.326855        84.21196
## 537    54.65899128          16.56408         51.863597        68.42768
## 538    37.74553596          26.67428         45.098214        71.77249
## 539    -6.91086002          55.78961         27.235656        83.02527
## 540    -5.74909768          43.22197         27.700361        70.92233
## 541    56.52824084          31.39191         52.611296        84.00320
## 542    40.30468000          27.52612         46.121872        73.64799
## 543    32.70843829          38.62955         43.083375        81.71292
## 544     6.82631958          33.73340         32.730528        66.46393
## 545    47.89912146          30.73781         49.159649        79.89746
## 546    -7.27585147          50.52923         27.089659        77.61889
## 547    50.72582315          27.36739         50.290329        77.65772
## 548    -8.05759377          52.39309         26.776962        79.17006
## 549    31.37837503          38.69049         42.551350        81.24184
## 550    56.11002105          22.96980         52.444008        75.41381
## 551    12.27594508          37.42588         34.910378        72.33626
## 552    57.51613877          20.42285         53.006456        73.42930
## 553    18.80639673          28.74675         37.522559        66.26931
## 554    11.85503772          46.83722         34.742015        81.57924
## 555    40.59072420          32.58545         46.236290        78.82174
## 556     7.84199121          39.94872         33.136796        73.08551
## 557    34.98404535          31.16181         43.993618        75.15543
## 558    28.24844226          37.83197         41.299377        79.13135
## 559     6.70356731          37.10280         32.681427        69.78423
## 560    22.85246480          36.18427         39.140986        75.32525
## 561    -4.75606205          39.26054         28.097575        67.35812
## 562    10.85782921          42.28930         34.343132        76.63243
## 563    41.17502548          20.78026         46.470010        67.25027
## 564    37.20312657          28.30508         44.881251        73.18634
## 565    -7.92290704          49.99542         26.830837        76.82626
## 566    55.97036601          22.82930         52.388146        75.21745
## 567    49.63912306          26.25831         49.855649        76.11396
## 568    58.81515937          33.10586         53.526064        86.63193
## 569    16.85478278          44.22369         36.741913        80.96561
## 570    -9.58604167          45.99599         26.165583        72.16157
## 571     2.58331912          40.58428         31.033328        71.61760
## 572    -1.00266313          44.34409         29.598935        73.94303
## 573    44.54195556          19.64455         47.816782        67.46133
## 574    18.81160539          35.25361         37.524642        72.77825
## 575    -4.91557341          41.50407         28.033771        69.53784
## 576    55.85077951          33.97710         52.340312        86.31741
## 577    57.97221786          27.93844         53.188887        81.12733
## 578    22.53387742          35.58977         39.013551        74.60332
## 579    56.76221507          20.23245         52.704886        72.93734
## 580    44.45423761          28.54623         47.781695        76.32792
## 581    35.89942685          30.72487         44.359771        75.08464
## 582    43.98057467          16.50790         47.592230        64.10013
## 583    32.06807322          32.36654         42.827229        75.19377
## 584    33.65743455          28.34876         43.462974        71.81173
## 585     7.87211966          47.22702         33.148848        80.37587
## 586    53.55097944          18.71051         51.420392        70.13091
## 587    -4.32633458          38.11425         28.269466        66.38372
## 588     8.44929126          45.51312         33.379717        78.89284
## 589    43.52809025          28.83488         47.411236        76.24611
## 590    59.11220655          19.88144         53.644883        73.52632
## 591     1.90160365          45.28138         30.760641        76.04202
## 592    50.04747638          22.68894         50.018991        72.70793
## 593     9.87856765          30.41989         33.951427        64.37132
## 594    43.91809738          27.68080         47.567239        75.24804
## 595    -1.77604263          40.40268         29.289583        69.69227
## 596     9.86287826          46.70705         33.945151        80.65220
## 597    -8.80052667          50.46932         26.479789        76.94911
## 598     3.41502681          33.80569         31.366011        65.17170
## 599    57.31210146          35.04772         52.924841        87.97256
## 600    12.04855803          34.03158         34.819423        68.85101
## 601    52.89146739          12.11107         51.156587        63.26766
## 602    20.70649138          37.80636         38.282597        76.08896
## 603    -7.55878811          52.67140         26.976485        79.64788
## 604     3.98502730          48.66239         31.594011        80.25640
## 605    32.80855564          30.47999         43.123422        73.60341
## 606     8.23796102          41.30790         33.295184        74.60309
## 607    15.86202360          37.12426         36.344809        73.46907
## 608    54.16979013          15.38328         51.667916        67.05120
## 609    29.03590285          24.12614         41.614361        65.74050
## 610    21.87049779          33.07549         38.748199        71.82369
## 611    58.95299231          18.89330         53.581197        72.47450
## 612    -9.36371965          45.61928         26.254512        71.87380
## 613    -3.79726234          43.43213         28.481095        71.91322
## 614    11.92417952          47.75631         34.769672        82.52598
## 615    33.22342111          22.07879         43.289368        65.36816
## 616    43.32460817          32.81237         47.329843        80.14221
## 617    43.66936617          23.42984         47.467746        70.89759
## 618    16.98113379          27.61750         36.792454        64.40995
## 619    48.43302465          29.77777         49.373210        79.15098
## 620     5.67530554          46.04081         32.270122        78.31093
## 621    14.73703343          35.31608         35.894813        71.21089
## 622    27.37697503          27.43686         40.950790        68.38765
## 623    59.26839940          18.75486         53.707360        72.46222
## 624    34.62107363          34.78995         43.848429        78.63838
## 625    21.76325471          22.97721         38.705302        61.68252
## 626     5.21959852          48.35522         32.087839        80.44306
## 627    33.19470026          33.37621         43.277880        76.65409
## 628     1.14733244          40.39758         30.458933        70.85651
## 629    57.56880772          17.32634         53.027523        70.35386
## 630    17.26261782          38.25942         36.905047        75.16446
## 631    -5.58568343          47.52531         27.765727        75.29104
## 632    58.16354734          10.56708         53.265419        63.83250
## 633    -6.38844788          48.37911         27.444621        75.82373
## 634    20.95010608          31.25045         38.380042        69.63050
## 635    47.89656926          31.48513         49.158628        80.64375
## 636     7.68608901          47.43613         33.074436        80.51056
## 637    25.03187798          32.89341         40.012751        72.90617
## 638     2.11967479          34.98403         30.847870        65.83190
## 639    16.57894959          28.26014         36.631580        64.89172
## 640    57.97412096          16.64649         53.189648        69.83614
## 641    42.30355075          29.68518         46.921420        76.60660
## 642     3.90254059          36.40497         31.561016        67.96599
## 643    33.63438446          25.35702         43.453754        68.81077
## 644    47.53616796          30.35751         49.014467        79.37198
## 645     3.16716294          40.72653         31.266865        71.99340
## 646    23.22769728          30.98708         39.291079        70.27816
## 647    -1.93167000          56.58382         29.227332        85.81115
## 648    24.14656985          42.44701         39.658628        82.10563
## 649     5.46969261          45.47182         32.187877        77.65970
## 650    47.73631030          25.48685         49.094524        74.58137
## 651     8.25067643          36.43451         33.300271        69.73478
## 652    44.59000673          19.90466         47.836003        67.74066
## 653    31.99263197          24.48198         42.797053        67.27903
## 654    44.07889126          18.48648         47.631557        66.11804
## 655    45.39232774          19.68365         48.156931        67.84058
## 656    55.45707325          27.83656         52.182829        80.01939
## 657    18.14014748          32.64077         37.256059        69.89683
## 658     3.37135000          41.06917         31.348540        72.41771
## 659    22.05532273          36.21930         38.822129        75.04143
## 660    42.74127647          19.95659         47.096511        67.05310
## 661    48.87835826          13.26050         49.551343        62.81184
## 662    31.77763424          32.00582         42.711054        74.71688
## 663    16.73386235          47.75627         36.693545        84.44982
## 664    24.59739088          40.55435         39.838956        80.39331
## 665    39.83212549          29.40185         45.932850        75.33470
## 666    58.67813909          21.13169         53.471256        74.60294
## 667    51.58862381          19.44275         50.635450        70.07820
## 668    55.49573886          21.32192         52.198296        73.52021
## 669    36.04467641          25.90380         44.417871        70.32167
## 670    20.82412381          43.57516         38.329650        81.90481
## 671    47.36963803          22.74003         48.947855        71.68789
## 672     5.27841176          47.93622         32.111365        80.04759
## 673    58.87774927          19.14430         53.551100        72.69540
## 674    34.42798660          29.58571         43.771195        73.35690
## 675    -9.26136531          56.92906         26.295454        83.22451
## 676    14.03755100          45.29930         35.615020        80.91432
## 677    14.66853627          34.89059         35.867415        70.75801
## 678    47.80103873          29.86743         49.120415        78.98784
## 679    -9.25467122          52.44936         26.298132        78.74749
## 680    11.67253510          32.96692         34.669014        67.63593
## 681    -7.74790903          52.38677         26.900836        79.28760
## 682    48.30087868          28.45022         49.320351        77.77057
## 683    21.88425941          27.21915         38.753704        65.97286
## 684    25.00511796          35.88493         40.002047        75.88698
## 685     7.37011492          43.38629         32.948046        76.33434
## 686    -5.68984228          47.31351         27.724063        75.03757
## 687    15.35310206          37.93269         36.141241        74.07394
## 688    31.74762579          26.68322         42.699050        69.38227
## 689    20.52438653          31.49863         38.209755        69.70838
## 690     0.64950381          44.01811         30.259802        74.27792
## 691    35.67126193          22.15612         44.268505        66.42463
## 692    20.75400034          35.80015         38.301600        74.10175
## 693     5.62298873          41.62736         32.249195        73.87656
## 694    -3.83620255          46.30170         28.465519        74.76722
## 695    29.09357766          24.39511         41.637431        66.03254
## 696    25.99445041          36.04329         40.397780        76.44107
## 697    38.42120922          23.99033         45.368484        69.35881
## 698     4.58612879          42.48695         31.834452        74.32140
## 699    26.06878121          35.45288         40.427512        75.88039
## 700     7.97834821          52.22699         33.191339        85.41833
## 701    50.96789549          28.40828         50.387158        78.79544
## 702    13.33324696          42.51851         35.333299        77.85181
## 703    21.90062279          32.10952         38.760249        70.86977
## 704    56.57396160          19.75320         52.629585        72.38278
## 705    11.21869300          41.17839         34.487477        75.66587
## 706    53.14576863          22.38858         51.258307        73.64689
## 707     2.72762839          43.38095         31.091051        74.47200
## 708    38.14783913          31.86851         45.259136        77.12764
## 709    23.04247289          25.37411         39.216989        64.59110
## 710    13.73824611          34.90440         35.495298        70.39970
## 711    13.17459572          36.79820         35.269838        72.06804
## 712    21.80312146          47.70712         38.721249        86.42837
## 713    54.48839070          22.19812         51.795356        73.99348
## 714    45.81171695          26.34944         48.324687        74.67412
## 715    21.24144557          48.41302         38.496578        86.90960
## 716    57.68317798          28.61101         53.073271        81.68428
## 717    42.68098362          17.17243         47.072393        64.24482
## 718    31.08456767          36.34688         42.433827        78.78071
## 719    45.31076307          31.20175         48.124305        79.32605
## 720    56.28718998          26.11055         52.514876        78.62542
## 721    53.81911605          25.52738         51.527646        77.05503
## 722     7.39054061          45.52632         32.956216        78.48254
## 723    46.84575806          29.14874         48.738303        77.88704
## 724    11.20084615          40.37352         34.480338        74.85386
## 725    22.42337598          34.85869         38.969350        73.82805
## 726    11.92155826          38.31859         34.768623        73.08721
## 727    20.56562671          33.52759         38.226251        71.75384
## 728     0.76861706          36.83630         30.307447        67.14375
## 729    45.31251092          26.59662         48.125004        74.72163
## 730    50.59893285          15.99256         50.239573        66.23214
## 731     0.45133606          42.83337         30.180534        73.01391
## 732    40.65552778          30.59642         46.262211        76.85863
## 733    51.51828443          26.49494         50.607314        77.10225
## 734    47.18381443          19.74098         48.873526        68.61451
## 735    10.60760694          38.33194         34.243043        72.57499
## 736     1.50788975          37.81458         30.603156        68.41774
## 737    55.91953926          16.01915         52.367816        68.38697
## 738     4.18923121          43.40281         31.675692        75.07850
## 739    43.79396285          25.72404         47.517585        73.24163
## 740    47.88156301          27.42515         49.152625        76.57777
## 741    10.42343448          37.64021         34.169374        71.80959
## 742    -4.11416220          45.99015         28.354335        74.34449
## 743    39.26618472          22.94351         45.706474        68.64998
## 744    56.47545044          16.04139         52.590180        68.63157
## 745    21.19317922          36.16399         38.477272        74.64126
## 746    56.39356842          25.36893         52.557427        77.92636
## 747    57.62312955          17.72395         53.049252        70.77320
## 748    36.76316727          29.24046         44.705267        73.94573
## 749    55.09533692          26.91598         52.038135        78.95411
## 750    17.83891072          43.51162         37.135564        80.64719
## 751    -9.72895248          51.08255         26.108419        77.19097
## 752    29.85677850          24.19996         41.942711        66.14267
## 753    -5.25861227          54.20675         27.896555        82.10330
## 754    -2.62733766          44.81473         28.949065        73.76379
## 755    22.95083637          26.35341         39.180335        65.53374
## 756     5.39161910          45.18902         32.156648        77.34567
## 757    26.01163372          31.91711         40.404653        72.32177
## 758    -1.53087209          45.15772         29.387651        74.54537
## 759    18.12139976          41.96061         37.248560        79.20917
## 760    42.96867194          20.12164         47.187469        67.30911
## 761    41.91950636          29.94806         46.767803        76.71586
## 762    22.19133318          45.62168         38.876533        84.49822
## 763    30.74303202          40.61340         42.297213        82.91061
## 764    44.32063950          23.66449         47.728256        71.39275
## 765    55.06142558          13.84438         52.024570        65.86895
## 766    33.70968845          30.43673         43.483875        73.92060
## 767    -5.40894299          44.33706         27.836423        72.17348
## 768     5.23825202          36.01729         32.095301        68.11259
## 769    31.79323794          39.62629         42.717295        82.34359
## 770    57.20311417          25.31550         52.881246        78.19674
## 771     3.66398494          39.92792         31.465594        71.39351
## 772    26.99224444          33.75158         40.796898        74.54848
## 773    31.29451483          27.92125         42.517806        70.43906
## 774    24.22564007          39.50323         39.690256        79.19349
## 775    37.81657222          35.42892         45.126629        80.55555
## 776    20.21312258          31.45439         38.085249        69.53964
## 777    13.69635518          39.05774         35.478542        74.53628
## 778    13.23125153          46.29698         35.292501        81.58948
## 779    -2.96820177          36.06896         28.812719        64.88168
## 780    38.83378592          26.78337         45.533514        72.31688
## 781    20.16483037          37.75621         38.065932        75.82214
## 782    52.50342017          21.95976         51.001368        72.96112
## 783    26.28344134          35.07488         40.513377        75.58825
## 784    56.62151238          16.71615         52.648605        69.36476
## 785    54.34863060          16.52957         51.739452        68.26903
## 786    30.61046475          34.69808         42.244186        76.94226
## 787    -1.22207134          30.88638         29.511171        60.39755
## 788    38.37788459          28.11931         45.351154        73.47047
## 789     9.14753620          43.08459         33.659014        76.74360
## 790    46.47984608          22.27451         48.591938        70.86645
## 791    36.40346398          30.24272         44.561386        74.80410
## 792    16.20886554          35.75921         36.483546        72.24276
## 793     5.98902110          45.43634         32.395608        77.83195
## 794    19.96463847          31.25168         37.985855        69.23753
## 795    35.88686411          30.11201         44.354746        74.46676
## 796    -8.29841420          44.62998         26.680634        71.31062
## 797    53.01167665          15.16361         51.204671        66.36828
## 798    57.23840809          19.68635         52.895363        72.58171
## 799     8.82574371          34.21870         33.530297        67.74899
## 800     4.56045402          40.83599         31.824182        72.66017
## 801    33.04756163          33.90167         43.219025        77.12069
## 802    20.23729327          30.72583         38.094917        68.82075
## 803    33.09828518          32.79795         43.239314        76.03726
## 804    -9.34423092          51.92597         26.262308        78.18828
## 805    43.69684457          19.37831         47.478738        66.85705
## 806    -8.62874476          42.21737         26.548502        68.76587
## 807    50.18825757          34.23967         50.075303        84.31497
## 808    -2.74923346          46.78099         28.900307        75.68130
## 809    -6.78410432          32.08069         27.286358        59.36705
## 810    -4.90593438          45.39735         28.037626        73.43498
## 811    44.59317972          22.45571         47.837272        70.29298
## 812     7.13524492          46.39274         32.854098        79.24684
## 813    29.36500014          35.09294         41.746000        76.83894
## 814    38.87157642          32.16453         45.548631        77.71316
## 815    10.42126806          44.89201         34.168507        79.06052
## 816    44.28437265          21.50605         47.713749        69.21980
## 817     6.73023629          39.92067         32.692095        72.61277
## 818    51.21069626          31.08641         50.484279        81.57069
## 819     7.27374071          31.97576         32.909496        64.88525
## 820    59.53907798          27.57964         53.815631        81.39527
## 821    26.08745474          37.16427         40.434982        77.59925
## 822     0.18644586          53.50090         30.074578        83.57548
## 823    -8.52893173          50.67350         26.588427        77.26193
## 824    35.63516752          23.49787         44.254067        67.75194
## 825    27.71136963          39.56448         41.084548        80.64903
## 826    45.98743412          23.89485         48.394974        72.28983
## 827    13.87985671          40.13132         35.551943        75.68326
## 828    23.22829692          43.22203         39.291319        82.51335
## 829    -5.93092650          38.04577         27.627629        65.67340
## 830    -1.43104848          51.37173         29.427581        80.79931
## 831     7.55588254          46.80942         33.022353        79.83178
## 832    38.93511956          20.86836         45.574048        66.44241
## 833    39.29548071          29.02638         45.718192        74.74457
## 834    26.39776989          30.26871         40.559108        70.82782
## 835    26.97179480          30.25831         40.788718        71.04702
## 836    36.77901249          32.77944         44.711605        77.49104
## 837     2.84836391          50.86728         31.139346        82.00662
## 838    46.97002536          23.23553         48.788010        72.02354
## 839     4.20985384          40.78051         31.683942        72.46446
## 840    26.92385239          28.91135         40.769541        69.68089
## 841    -0.15169964          37.81900         29.939320        67.75832
## 842    57.85779033          16.23407         53.143116        69.37719
## 843    34.64888760          29.48244         43.859555        73.34200
## 844    11.66816287          46.40075         34.667265        81.06802
## 845    34.68646865          32.30113         43.874587        76.17572
## 846    21.47188594          40.07615         38.588754        78.66491
## 847    -4.46130480          47.58384         28.215478        75.79932
## 848    59.00068807          17.06703         53.600275        70.66730
## 849    33.70789161          27.86916         43.483157        71.35232
## 850    20.60185028          41.47064         38.240740        79.71138
## 851    44.64247840          38.48638         47.856991        86.34337
## 852    35.25224620          23.21236         44.100898        67.31325
## 853     3.90358876          40.61215         31.561436        72.17359
## 854     9.38879679          34.90259         33.755519        68.65810
## 855    26.60399366          34.38923         40.641597        75.03083
## 856    41.33236441          34.80813         46.532946        81.34108
## 857    48.94764075          19.79005         49.579056        69.36910
## 858    54.88408126          26.59124         51.953633        78.54487
## 859    17.05293376          34.88652         36.821174        71.70769
## 860    41.78318934          36.59477         46.713276        83.30804
## 861    22.68645743          41.17437         39.074583        80.24895
## 862    16.35150558          30.61402         36.540602        67.15462
## 863    35.93922174          27.08265         44.375689        71.45834
## 864    30.19617431          31.52115         42.078470        73.59962
## 865    52.76925183          23.50494         51.107701        74.61264
## 866    36.31799410          36.41909         44.527198        80.94629
## 867    57.19360809          15.67198         52.877443        68.54943
## 868    16.19069478          43.43378         36.476278        79.91006
## 869    25.59940638          32.49900         40.239763        72.73877
## 870     4.51388458          40.98800         31.805554        72.79355
## 871    -5.56265387          40.41075         27.774938        68.18569
## 872    37.98331320          31.79675         45.193325        76.99007
## 873    48.27705164          26.74678         49.310821        76.05760
## 874    41.72914782          30.28198         46.691659        76.97364
## 875     4.12670328          48.46257         31.650681        80.11325
## 876    38.27295686          33.25832         45.309183        78.56751
## 877     0.92381279          41.61665         30.369525        71.98617
## 878    53.51516958          16.62168         51.406068        68.02775
## 879    33.03164609          23.05200         43.212658        66.26466
## 880     0.03016346          47.19642         30.012065        77.20848
## 881    36.80788981          24.03996         44.723156        68.76311
## 882    -5.26876849          48.50404         27.892493        76.39653
## 883    49.29346108          33.47121         49.717384        83.18860
## 884    38.69345384          28.51835         45.477382        73.99573
## 885    53.35903740          20.22864         51.343615        71.57226
## 886    23.95671318          25.97501         39.582685        65.55770
## 887    58.99367850          24.12381         53.597471        77.72128
## 888    26.64732747          30.51966         40.658931        71.17859
## 889    38.98181339          34.42363         45.592725        80.01636
## 890    24.71826857          30.88222         39.887307        70.76952
## 891    50.70018713          31.48477         50.280075        81.76485
## 892    36.36638942          34.94235         44.546556        79.48890
## 893    32.63239437          34.22036         43.052958        77.27331
## 894     2.63083118          36.74777         31.052332        67.80010
## 895    18.43415412          27.02362         37.373662        64.39728
## 896    31.82795837          36.02330         42.731183        78.75448
## 897    -2.74241145          42.41454         28.903035        71.31757
## 898    59.73181562          15.25998         53.892726        69.15271
## 899    40.94520740          23.14727         46.378083        69.52535
## 900    37.72422433          31.17298         45.089690        76.26267
## 901    42.21568067          32.01866         46.886272        78.90494
## 902    26.83041406          26.77632         40.732166        67.50848
## 903    35.43787366          32.12870         44.175149        76.30385
## 904     1.90628891          47.22102         30.762516        77.98354
## 905    38.31260780          29.94314         45.325043        75.26818
## 906    31.01956729          34.26794         42.407827        76.67577
## 907    -9.80684887          43.20964         26.077260        69.28690
## 908    39.32568977          28.68301         45.730276        74.41329
## 909    52.24686890          20.51676         50.898748        71.41551
## 910    40.90772962          21.83249         46.363092        68.19558
## 911    28.98280300          33.99475         41.593121        75.58787
## 912    54.17878126          17.16892         51.671513        68.84043
## 913    32.10790131          29.37164         42.843161        72.21480
## 914    54.63678406          17.34716         51.854714        69.20188
## 915    -9.04105458          50.84280         26.383578        77.22638
## 916     2.95583759          40.56978         31.182335        71.75211
## 917     5.65147389          39.48817         32.260590        71.74876
## 918    42.92435663          27.16771         47.169743        74.33745
## 919    53.72941694          22.72208         51.491767        74.21384
## 920    51.86737113          19.64785         50.746948        70.39480
## 921    25.82485060          36.14906         40.329940        76.47900
## 922    25.54569174          43.81366         40.218277        84.03193
## 923    56.94678385          20.26746         52.778714        73.04617
## 924    52.75352698          28.82017         51.101411        79.92158
## 925    47.53786727          32.12464         49.015147        81.13979
## 926     3.13531956          49.44198         31.254128        80.69611
## 927    49.07622840          18.10466         49.630491        67.73515
## 928    19.38015102          41.09908         37.752060        78.85114
## 929    19.80056661          26.86976         37.920227        64.78999
## 930    32.84491949          29.80049         43.137968        72.93846
## 931    -3.48142360          47.59833         28.607431        76.20576
## 932    -2.65123198          49.80337         28.939507        78.74288
## 933    40.30445281          26.32183         46.121781        72.44361
## 934    22.35197746          31.82111         38.940791        70.76190
## 935    -0.61394783          45.08844         29.754421        74.84286
## 936     1.51007709          39.23008         30.604031        69.83411
## 937    14.64076282          33.11418         35.856305        68.97048
## 938    21.98762474          33.45349         38.795050        72.24854
## 939     4.82871603          45.26007         31.931486        77.19155
## 940     3.88749967          34.71150         31.555000        66.26650
## 941    -2.93955205          39.87854         28.824179        68.70272
## 942    51.19039149          18.59577         50.476157        69.07193
## 943    51.51981481          24.39418         50.607926        75.00211
## 944    39.12508001          23.09569         45.650032        68.74573
## 945    32.47448948          27.51672         42.989796        70.50651
## 946    53.68943040          27.28845         51.475772        78.76422
## 947    26.51746927          29.01549         40.606988        69.62248
## 948    46.98920819          17.70710         48.795683        66.50278
## 949     4.30882137          43.01295         31.723529        74.73648
## 950    26.46387181          33.11213         40.585549        73.69768
## 951    15.33481458          39.53522         36.133926        75.66914
## 952    -0.54129589          49.65739         29.783482        79.44088
## 953    -2.93809571          32.94181         28.824762        61.76657
## 954    10.96300656          44.30219         34.385203        78.68739
## 955     1.24477323          52.25154         30.497909        82.74945
## 956    -5.82493194          36.89550         27.670027        64.56553
## 957    56.50617960          16.33668         52.602472        68.93915
## 958    42.87602603          23.23409         47.150410        70.38450
## 959     1.08046291          41.02908         30.432185        71.46127
## 960    32.52673153          25.40959         43.010693        68.42028
## 961    32.51417364          32.67341         43.005669        75.67908
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## 999          TRUE        FALSE
## 1000         TRUE        FALSE

2SLS

We could manually run the first stage model, generate predicted tutoring and then use those predicted values in the second stage model like we did in the instrumental variables example, but that’s tedious and nobody wants to do all that work. We’ll use iv_robust() from the estimatr package instead.

Note: be careful! if there are missing values (in D), you may fail to replicate the fuzzy effect by hand sum(is.na(crab_data$fished)) #ok for the simulated data

Instead, we need to run a 2SLS model that includes our instrument in the first stage, which will then remove the endogeneity built into participation in the program. We’ll estimate this set of models:

##NEED TO FINISHED - IS THIS RIGHT??? \[ \begin{aligned} \widehat{\text{Fished}} &= \gamma_0 + \gamma_1 \text{Size}_\text{centered} + \gamma_2 \text{Below cutoff} + \omega \\ \text{Fishing Mortality} &= \beta_0 + \beta_1 \text{Size}_\text{centered} + \beta_2 \widehat{\text{Fished}} + \epsilon \end{aligned} \]

Fuzzy nonparametric estimation

We can also use nonparametric methods to measure the size of the fuzzy gap at the cutoff. We’ll use rdrobust(). T

To do fuzzy estimation with rdrobust(), use the fuzzy argument to specify the treatment column (or fished in our case). Importantly (and confusingly! this took me waaaaay too long to figure out!), you do not need to specify an instrument (or even create one!). All you need to specify is the column that indicates treatment status—rdrobust() will do all the above/below-the-cutoff instrument stuff behind the scenes for you.

##NEED TO FINISHED WITH IV CREATED AS ENTRANCE EXAM

rdrobust(y = crab_data$fishing_mortality, x = crab_data$size_centered,
         c = 0, fuzzy = crab_data$fished) %>%
  summary()

## Fuzzy RD estimates using local polynomial regression.
## 
## Number of Obs.                 1000
## BW type                       mserd
## Kernel                   Triangular
## VCE method                       NN
## 
## Number of Obs.                  480          520
## Eff. Number of Obs.             121          142
## Order est. (p)                    1            1
## Order bias  (q)                   2            2
## BW est. (h)                   8.850        8.850
## BW bias (b)                  17.518       17.518
## rho (h/b)                     0.505        0.505
## Unique Obs.                     480          520
## 
## First-stage estimates.
## 
## =============================================================================
##         Method     Coef. Std. Err.         z     P>|z|      [ 95% C.I. ]       
## =============================================================================
##   Conventional     0.117     0.156     0.750     0.453    [-0.188 , 0.422]     
##         Robust         -         -     1.143     0.253    [-0.143 , 0.543]     
## =============================================================================
## 
## Treatment effect estimates.
## 
## =============================================================================
##         Method     Coef. Std. Err.         z     P>|z|      [ 95% C.I. ]       
## =============================================================================
##   Conventional    20.944     1.687    12.413     0.000    [17.637 , 24.251]    
##         Robust         -         -    10.491     0.000    [16.939 , 24.722]    
## =============================================================================

That’s all! Using nonparametric methods, with a triangular kernel and a bandwidth of ±12.96, the causal effect of the tutoring program for compliers in the bandwidth is 9.683.

We can (and should!) do all the other nonparametric robustness checks that we talked about in the regression discontinuity example, like modifying the bandwidth (ideal, half, double) and messing with the kernel (uniform, triangular, Epanechnikov) to see how robust the finding is. But again, we won’t do any of that here.

Useful references and websites for more resources

https://dimewiki.worldbank.org/Regression_Discontinuity

the MixTape by Scott Cummingham: https://mixtape.scunning.com/06-regression_discontinuity

RDD with interactions: https://www.jepusto.com/rdd-interactions/

Simulate Data

Modified from the MixTape by Scott Cummingham: https://mixtape.scunning.com/06-regression_discontinuity

library(tidyverse)
# simulate the data
dat <- tibble(
  x = rnorm(1000, 50, 25)
) %>%
  mutate(
    x = if_else(x < 0, 0, x)
  ) %>%
  filter(x < 100)

# cutoff at x = 70, no jump
dat <- dat %>% 
  mutate(
    D  = if_else(x > 70, 1, 0),
    y1 = 25 + 0 * D + 1.5 * x + rnorm(n(), 0, 20)
  )

ggplot(aes(x, y1, colour = factor(D)), data = dat) +
  geom_point(alpha = 0.5) +
  geom_vline(xintercept = 70, colour = "grey", linetype = 2)+
  stat_smooth(method = "lm", se = F) +
  labs(x = "Test score (X)", y = "Potential Outcome (Y1)")

## `geom_smooth()` using formula = 'y ~ x'

## simulate the discontinuity
dat <- dat %>%
  mutate(
    y2 = 25 + 40 * D + 1.5 * x + rnorm(n(), 0, 20)
  )

# figure
ggplot(aes(x, y2, colour = factor(D)), data = dat) +
  geom_point(alpha = 0.5) +
  geom_vline(xintercept = 70, colour = "grey", linetype = 2) +
  stat_smooth(method = "lm", se = F) +
  labs(x = "Test score (X)", y = "Potential Outcome (Y)")

## `geom_smooth()` using formula = 'y ~ x'

# simultate nonlinearity
dat <- tibble(
    x = rnorm(1000, 100, 50)
  ) %>% 
  mutate(
    x = case_when(x < 0 ~ 0, TRUE ~ x),
    D = case_when(x > 140 ~ 1, TRUE ~ 0),
    x2 = x*x,
    x3 = x*x*x,
    y3 = 10000 + 0 * D - 100 * x + x2 + rnorm(1000, 0, 1000)
  ) %>% 
  filter(x < 280)

ggplot(aes(x, y3, colour = factor(D)), data = dat) +
  geom_point(alpha = 0.2) +
  geom_vline(xintercept = 140, colour = "grey", linetype = 2) +
  stat_smooth(method = "lm", se = F) +
  labs(x = "Test score (X)", y = "Potential Outcome (Y)")

## `geom_smooth()` using formula = 'y ~ x'

ggplot(aes(x, y3, colour = factor(D)), data = dat) +
  geom_point(alpha = 0.2) +
  geom_vline(xintercept = 140, colour = "grey", linetype = 2) +
  stat_smooth(method = "loess", se = F) +
  labs(x = "Test score (X)", y = "Potential Outcome (Y)")

## `geom_smooth()` using formula = 'y ~ x'

–>

We can check the size two different ways: parametrically (i.e. using lm() with specific parameters and coefficients), and nonparametrically (i.e. not using lm() or any kind of straight line and instead drawing lines that fit the data more precisely). We’ll do it both ways.

Parametric estimation

First we’ll do it parametrically by using linear regression. Here we want to explain the variation in final scores based on the entrance exam score and participation in the tutoring program:

\[ \text{Exit exam} = \beta_0 + \beta_1 \text{Entrance exam score}_\text{centered} + \beta_2 \text{Tutoring program} + \epsilon \]

Nonparametric estimation

Instead of using linear regression to measure the size of the discontinuity, we can use nonparametric methods. Essentially this means that R will not try to fit a straight line to the data—instead it’ll curve around the points and try to fit everything as smoothly as possible.

The rdrobust() function makes it really easy to measure the gap at the cutoff with nonparametric estimation. Here’s the simplest version: